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Moncef Abbas

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Dominique Lepelley

Université de la Réunion

Harishchandra Dubey

Microsoft

Professor Mohamed H . Gadallah

Cairo University Egypt

University of the National Education Commission in Krakow

Silvia Regina Vergilio

Milos Pejanovic

Argimiro R. Secchi

Universidade Federal do Rio de Janeiro (UFRJ)

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Papers by Moncef Abbas

Contribution to Solving a Two-Dimensional Cutting Stock Problem with Two Objectives

Economic Computation and Economic Cybernetics Studies and Research, Jun 20, 2022

In this paper, we propose a technique for solving a twodimensional cutting stock problem with two... more In this paper, we propose a technique for solving a twodimensional cutting stock problem with two-objective. It's about cutting a number of rectangular pieces from a set of raw material plates, themselves identical. These are available in unlimited quantities, where we try to minimize the total area lost and the number of setups to be carried out. This technique is made up of two stages, the first of which consists in generating all the feasible cutting patterns and the second makes it possible to construct cutting plans, satisfying the demands, thanks to a subset of these patterns. These different cutting plans represent all the feasible solutions, each of which is characterized by a number of setups and the total quantity of falls.

Minimizing the Makespan in a Robotic Cell Scheduling Problem

$Research paper thumbnail of An algorithm for mixed integer linear fractional programming problems$

An algorithm for mixed integer linear fractional programming problems

ABSTRACT

Contribution to Solving a Two-Dimensional Cutting Stock Problem with Two Objectives

ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH

In this paper, we propose a technique for solving a twodimensional cutting stock problem with two... more In this paper, we propose a technique for solving a twodimensional cutting stock problem with two-objective. It's about cutting a number of rectangular pieces from a set of raw material plates, themselves identical. These are available in unlimited quantities, where we try to minimize the total area lost and the number of setups to be carried out. This technique is made up of two stages, the first of which consists in generating all the feasible cutting patterns and the second makes it possible to construct cutting plans, satisfying the demands, thanks to a subset of these patterns. These different cutting plans represent all the feasible solutions, each of which is characterized by a number of setups and the total quantity of falls.

New Hierarchical Clustering Method in Interval Data

In computer science, various clustering algorithms have been developed since conventional hierarc... more In computer science, various clustering algorithms have been developed since conventional hierarchical cluster analysis (HCA), which aims to discover a consistent hierarchy of clusters with different granularities (partitions). In hierarchical clustering, has properties to the representation as tree named dendrogram where each node is associated with merging of two (or more) partitions, where are useful for the interpretation of clustering results and their visualization. Many clustering algorithms have been developed since conventional HCA but are limited in the application. However, the conventional clustering algorithms (mostly HCA) still play an important role. In this paper, we introduce a new ranking based hierarchical clustering on an interval data set with the help of dominance relation, which is efficient to improve ranking clustering accuracy. In each iteration, first a directional distance is calculated on the original data interval. An individu is then created on the sel...

Contribution to solving a one-dimensional cutting stock problem with two objectives based on the generation of cutting patterns

Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA

Performance of multicriteria decision making methods: study and cases

International Journal of Multicriteria Decision Making, 2017

In this paper, the problematic of MCDM methods evaluation is treated, we study in particular the ... more In this paper, the problematic of MCDM methods evaluation is treated, we study in particular the behaviour of the criteria (tests) measuring the performance of these methods. Indeed, a critical study toward the series of tests proposed by Triantaphyllou is carried out. On this basis, some impossibility results are defined. In addition, a new assessment test is proposed.

Reference Points in TOPSIS Methods for Group Decision Makers & Interval Data: Study and Comparison

In this paper, two new extensions of TOPSIS method for Group decision makers and Interval data ar... more In this paper, two new extensions of TOPSIS method for Group decision makers and Interval data are presented. In particular, the behavior of some past contributions when using Nadir point at the place of anti ideal point is studied. Otherwise, through simulation studies and simulation, which are mainly based upon smart random instances, a comparison between four algorithms is carried out, its purpose is to show the most effective one.

Penalties Method for Integer Linear Fractional Programs

ABSTRACT

A morphological analysis of Arabic language based on multicriteria decision making: TAGHIT system

2010 International Conference on Machine and Web Intelligence, 2010

Abstract In this paper, we present our work on Arabic morphology and especially the mechanisms fo... more Abstract In this paper, we present our work on Arabic morphology and especially the mechanisms for resolving the morphological ambiguity in Arabic text. These researches, which have given birth to TAGHIT system which is a morphosyntactic tagger for Arabic, where the originality of our work lies in the implementation of our internal system of a new approach to disambiguation different from those that currently exist, which is based on the principles and techniques issued from multicriteria decision making.

Analyse de l'imprécision du taux de défaillance de cause commune pour l'évaluation des performances des SIS

Dans cet article, le problème d'imprécision dans l'évaluation de la performance des systèmes inst... more Dans cet article, le problème d'imprécision dans l'évaluation de la performance des systèmes instrumentés de sécurité est traité. Deux méthodes d'évaluation sont appliquées sur un exemple. La première méthode d'évaluation utilise les arbres de défaillances, la seconde se base sur les chaînes de Markov. Les paramètres caractéristiques des SIS, tels que le facteur de défaillance de cause commune sont remplacées par des nombres flous permettant aux experts fiabilistes d'exprimer leur incertitude dans l'énoncé des valeurs de probabilités de défaillances et autres paramètres des systèmes. Nous montrons comment l'imprécision sur la valeur de taux de défaillance de cause commune, induit des variations particulièrement significatives sur la qualification du niveau d'intégrité de sécurité d'un SIS et ainsi l'intérêt pour le décideur de connaître l'imprécision sur le paramètre de performance.

A DDoS Attack Detection System: Applying A Hybrid Genetic Algorithm to Optimal Feature Subset Selection

2020 4th International Symposium on Informatics and its Applications (ISIA), 2020

The rapid evolution in technology is a great challenge for network security against computer thre... more The rapid evolution in technology is a great challenge for network security against computer threats. Indeed, distributed denial of service (DDoS) attacks aim to deplete or even cripple target networks with malicious traffic. However, before they can be dealt with, these attacks must be identified through real-time analysis of the NetFlow sent by the routers. A large amount of flow during attacks requires the design of a standalone detector with high capacity to support this load and capable of processing traffic in real-time but with low computation time. For the same purpose, detectors based on machine learning suffer from being uncompetitive because they produce many false positives and above all require a lot of computing resources. In order to overcome these problems, in this article, we propose DDoS-Detector, a new identification and detection system, we identify the most relevant features of malicious traffic and develop a suitable concept for real-time DDoS detection.

Encrypted Traffic Classification: Combining Over-and Under-Sampling through a PCA-SVM

2018 3rd International Conference on Pattern Analysis and Intelligent Systems (PAIS), 2018

VPN (Virtual Private Network) is often the most efficient and the least expensive way to maintain... more VPN (Virtual Private Network) is often the most efficient and the least expensive way to maintain flexibility, integrity and confidentiality of data exchange over the Internet. It also enables users to establish private and secure connections and avoid the common geographical restrictions of certain services offered on the net. In this context, the Deep Packet Inspection techniques (DPIs) enable firewalls to filter the VPN traffic when it is not encrypted. Otherwise, it becomes difficult to do so. In this paper, we propose a method for characterizing the traffic in one step i.e., without previously dividing VPN from non-VPN. Instead, we combine over- and under-sampling followed by Principal Component Analysis (PCA). This approach allows selecting the optimum feature subset before performing an efficient traffic classification using Support Vectors Machines classifier. In order to assess our findings, 14 types of traffic were used: 7 encrypted and 7 VPN traffic categories. Accordingly, we used only time-based flow-based features. We checked the effectiveness and performances of our proposal through several experiments of different generated timeout flows of durations on the UNB ISCX data set.

The impact of using new significant reference point with TOPSIS methods: study and application

International Journal of Information and Decision Sciences, 2019

In this paper, the impact of Pareto optimality concept on revised TOPSIS method is studied. In pa... more In this paper, the impact of Pareto optimality concept on revised TOPSIS method is studied. In particular, we study theoretically the cases in which a preference relation changes when delimiting the choice of the best alternative(s) in an efficient restrictive area. In order to define the most reliable approach a comparative study is established. On this basis, an accurate new method called TOPSIS Nadir is introduced. Furthermore, an adaptation for interval data area is carried out in which we discuss some forms of normalisation. By following the same steps of the TOPSIS methods for group decision makers, we develop and compare two new procedures.

Two-dimensional Intrusion Detection System: A New Feature Selection Technique

2020 2nd International Workshop on Human-Centric Smart Environments for Health and Well-being (IHSH)

The rapid increase and expansion of cyber-attacks requires the development of new quality tools t... more The rapid increase and expansion of cyber-attacks requires the development of new quality tools to reduce, combat, and eventually stop their risks. In this context, an Intrusion Prevention Systems (IPS) is introduced. It is an extended IDS solutions network security technology characterized by adding the ability to block threats and detect vulnerabilities exploits. Unlike its predecessor, the IPS is placed as an inline security component where it actively processes via analyzing and taking automated actions on all traffic flows that enter the network. Needless to say, speed and efficiency are a necessity in the IPS to avoid degrading network performance. On one hand, signature-based detection and statistical anomaly-based detection, two dominant detection methods mechanisms, are responsible for finding exploits whenever statistical features are extracted to characterize network traffic flows. The computation cost of the classifier, therefore, will be overlarge. On the other hand, the feature selection problem, a critical component in reducing features and improving overall classification accuracy, is about a highly complex NP-hard problem in a Data science. In this paper, a novel intrusion detection system is proposed. It is a double-action system with meta-classifier based feature selection as well as an ensemble learning meta-classifier for stacking via cross-validation to prevent overfitting. Therefore, a better subset of informative features for each type of attacks was selected rather than the features common to all attacks. Finally, this work, through the several experiments, demonstrates that our proposed model not only reaches high detection rates and significantly reduces false alarms, but also accelerates the learning and the testing process thereby directly contributing to the overall ability to work in online mode and scalability.

The Prague Bulletin of Mathematical Linguistics Towards a New Approach for Disambiguation in NLP by Multiple Criterian Decision-Aid

The aim of this paper is to present a combination of NLP and Multiple Criteria Decision-Aid (MCDA... more The aim of this paper is to present a combination of NLP and Multiple Criteria Decision-Aid (MCDA) in order to reach an effective analysis when dealing with linguistic data from various sources. The coexistence of these two concepts has allowed us, based on a set of actions and criteria, to develop a coherent system that integrates the entire process of textual data analysis (no-voweled Arabic texts) into decision making in case of ambiguity. Our solution is based on decision theory and an MCDA approach with a TOPSIS technique. This method allows the multi-scenario classification of morphosyntactical ambiguity cases in order to come out with the best performance and reduce the number of candidate scenarios.

Packing chromatic numbers of finite super subdivisions of graphs

Filomat, 2020

Given a graph G and a positive integer i, an i-packing in G is a subset W of the vertex set of G ... more Given a graph G and a positive integer i, an i-packing in G is a subset W of the vertex set of G such that the distance between any two distinct vertices from W is greater than i. The packing chromatic number of a graph G, ??(G), is the smallest integer k such that the vertex set of G can be partitioned into sets Vi, i ? {1,..., k}, where each Vi is an i-packing. In this paper, we present some general properties of packing chromatic numbers of finite super subdivisions of graphs. We determine the packing chromatic numbers of the finite super subdivisions of complete graphs, cycles and some neighborhood corona graphs.

TAGHIT: Un étiqueteur Morphosyntaxique de l’Arabe Basé sur une Approche Multicritère

Makespan minimization for two-stage hybrid Flow shop with dedicated machines and additional constraints

This paper considers a two-stage hybrid flow shop scheduling problem. The objective is the minimi... more This paper considers a two-stage hybrid flow shop scheduling problem. The objective is the minimizing of maximum completion time of all the jobs. There exist two dedicated machines at stage 1 and one machine at stage 2. Each job is defined by two operations processed on the two-stages in series. Depending on the job type, the job is processed on either of the two machines at stage1 and must be processed on the single machine at stage2. the jobs are transported between the stages by a robot or a conveyor. After the problem formulation, we present lower bounds for the objective function. We then discuss a few polynomially solvable cases of the problem and present the solution algorithms. Since a general case of the problem is strongly NP-hard, we propose two heuristics to find approximate solutions to the general case. Computational experiments are done on a number of randomly generated test problems, and the test results are reported.

On locating chromatic number of Möbius ladder graphs

Proyecciones (Antofagasta), 2021

In this paper, we are dealing with the study of locating chromatic number of Möbius-ladders. We p... more

Contribution to Solving a Two-Dimensional Cutting Stock Problem with Two Objectives

Economic Computation and Economic Cybernetics Studies and Research, Jun 20, 2022

In this paper, we propose a technique for solving a twodimensional cutting stock problem with two... more In this paper, we propose a technique for solving a twodimensional cutting stock problem with two-objective. It's about cutting a number of rectangular pieces from a set of raw material plates, themselves identical. These are available in unlimited quantities, where we try to minimize the total area lost and the number of setups to be carried out. This technique is made up of two stages, the first of which consists in generating all the feasible cutting patterns and the second makes it possible to construct cutting plans, satisfying the demands, thanks to a subset of these patterns. These different cutting plans represent all the feasible solutions, each of which is characterized by a number of setups and the total quantity of falls.

Minimizing the Makespan in a Robotic Cell Scheduling Problem

$Research paper thumbnail of An algorithm for mixed integer linear fractional programming problems$

An algorithm for mixed integer linear fractional programming problems

ABSTRACT

Contribution to Solving a Two-Dimensional Cutting Stock Problem with Two Objectives

ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH

In this paper, we propose a technique for solving a twodimensional cutting stock problem with two... more In this paper, we propose a technique for solving a twodimensional cutting stock problem with two-objective. It's about cutting a number of rectangular pieces from a set of raw material plates, themselves identical. These are available in unlimited quantities, where we try to minimize the total area lost and the number of setups to be carried out. This technique is made up of two stages, the first of which consists in generating all the feasible cutting patterns and the second makes it possible to construct cutting plans, satisfying the demands, thanks to a subset of these patterns. These different cutting plans represent all the feasible solutions, each of which is characterized by a number of setups and the total quantity of falls.

New Hierarchical Clustering Method in Interval Data

In computer science, various clustering algorithms have been developed since conventional hierarc... more In computer science, various clustering algorithms have been developed since conventional hierarchical cluster analysis (HCA), which aims to discover a consistent hierarchy of clusters with different granularities (partitions). In hierarchical clustering, has properties to the representation as tree named dendrogram where each node is associated with merging of two (or more) partitions, where are useful for the interpretation of clustering results and their visualization. Many clustering algorithms have been developed since conventional HCA but are limited in the application. However, the conventional clustering algorithms (mostly HCA) still play an important role. In this paper, we introduce a new ranking based hierarchical clustering on an interval data set with the help of dominance relation, which is efficient to improve ranking clustering accuracy. In each iteration, first a directional distance is calculated on the original data interval. An individu is then created on the sel...

Contribution to solving a one-dimensional cutting stock problem with two objectives based on the generation of cutting patterns

Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA

Performance of multicriteria decision making methods: study and cases

International Journal of Multicriteria Decision Making, 2017

In this paper, the problematic of MCDM methods evaluation is treated, we study in particular the ... more In this paper, the problematic of MCDM methods evaluation is treated, we study in particular the behaviour of the criteria (tests) measuring the performance of these methods. Indeed, a critical study toward the series of tests proposed by Triantaphyllou is carried out. On this basis, some impossibility results are defined. In addition, a new assessment test is proposed.

Reference Points in TOPSIS Methods for Group Decision Makers & Interval Data: Study and Comparison

In this paper, two new extensions of TOPSIS method for Group decision makers and Interval data ar... more In this paper, two new extensions of TOPSIS method for Group decision makers and Interval data are presented. In particular, the behavior of some past contributions when using Nadir point at the place of anti ideal point is studied. Otherwise, through simulation studies and simulation, which are mainly based upon smart random instances, a comparison between four algorithms is carried out, its purpose is to show the most effective one.

Penalties Method for Integer Linear Fractional Programs

ABSTRACT

A morphological analysis of Arabic language based on multicriteria decision making: TAGHIT system

2010 International Conference on Machine and Web Intelligence, 2010

Abstract In this paper, we present our work on Arabic morphology and especially the mechanisms fo... more Abstract In this paper, we present our work on Arabic morphology and especially the mechanisms for resolving the morphological ambiguity in Arabic text. These researches, which have given birth to TAGHIT system which is a morphosyntactic tagger for Arabic, where the originality of our work lies in the implementation of our internal system of a new approach to disambiguation different from those that currently exist, which is based on the principles and techniques issued from multicriteria decision making.

Analyse de l'imprécision du taux de défaillance de cause commune pour l'évaluation des performances des SIS

Dans cet article, le problème d'imprécision dans l'évaluation de la performance des systèmes inst... more Dans cet article, le problème d'imprécision dans l'évaluation de la performance des systèmes instrumentés de sécurité est traité. Deux méthodes d'évaluation sont appliquées sur un exemple. La première méthode d'évaluation utilise les arbres de défaillances, la seconde se base sur les chaînes de Markov. Les paramètres caractéristiques des SIS, tels que le facteur de défaillance de cause commune sont remplacées par des nombres flous permettant aux experts fiabilistes d'exprimer leur incertitude dans l'énoncé des valeurs de probabilités de défaillances et autres paramètres des systèmes. Nous montrons comment l'imprécision sur la valeur de taux de défaillance de cause commune, induit des variations particulièrement significatives sur la qualification du niveau d'intégrité de sécurité d'un SIS et ainsi l'intérêt pour le décideur de connaître l'imprécision sur le paramètre de performance.

A DDoS Attack Detection System: Applying A Hybrid Genetic Algorithm to Optimal Feature Subset Selection

2020 4th International Symposium on Informatics and its Applications (ISIA), 2020

The rapid evolution in technology is a great challenge for network security against computer thre... more The rapid evolution in technology is a great challenge for network security against computer threats. Indeed, distributed denial of service (DDoS) attacks aim to deplete or even cripple target networks with malicious traffic. However, before they can be dealt with, these attacks must be identified through real-time analysis of the NetFlow sent by the routers. A large amount of flow during attacks requires the design of a standalone detector with high capacity to support this load and capable of processing traffic in real-time but with low computation time. For the same purpose, detectors based on machine learning suffer from being uncompetitive because they produce many false positives and above all require a lot of computing resources. In order to overcome these problems, in this article, we propose DDoS-Detector, a new identification and detection system, we identify the most relevant features of malicious traffic and develop a suitable concept for real-time DDoS detection.

Encrypted Traffic Classification: Combining Over-and Under-Sampling through a PCA-SVM

2018 3rd International Conference on Pattern Analysis and Intelligent Systems (PAIS), 2018

VPN (Virtual Private Network) is often the most efficient and the least expensive way to maintain... more VPN (Virtual Private Network) is often the most efficient and the least expensive way to maintain flexibility, integrity and confidentiality of data exchange over the Internet. It also enables users to establish private and secure connections and avoid the common geographical restrictions of certain services offered on the net. In this context, the Deep Packet Inspection techniques (DPIs) enable firewalls to filter the VPN traffic when it is not encrypted. Otherwise, it becomes difficult to do so. In this paper, we propose a method for characterizing the traffic in one step i.e., without previously dividing VPN from non-VPN. Instead, we combine over- and under-sampling followed by Principal Component Analysis (PCA). This approach allows selecting the optimum feature subset before performing an efficient traffic classification using Support Vectors Machines classifier. In order to assess our findings, 14 types of traffic were used: 7 encrypted and 7 VPN traffic categories. Accordingly, we used only time-based flow-based features. We checked the effectiveness and performances of our proposal through several experiments of different generated timeout flows of durations on the UNB ISCX data set.

The impact of using new significant reference point with TOPSIS methods: study and application

International Journal of Information and Decision Sciences, 2019

In this paper, the impact of Pareto optimality concept on revised TOPSIS method is studied. In pa... more In this paper, the impact of Pareto optimality concept on revised TOPSIS method is studied. In particular, we study theoretically the cases in which a preference relation changes when delimiting the choice of the best alternative(s) in an efficient restrictive area. In order to define the most reliable approach a comparative study is established. On this basis, an accurate new method called TOPSIS Nadir is introduced. Furthermore, an adaptation for interval data area is carried out in which we discuss some forms of normalisation. By following the same steps of the TOPSIS methods for group decision makers, we develop and compare two new procedures.

Two-dimensional Intrusion Detection System: A New Feature Selection Technique

2020 2nd International Workshop on Human-Centric Smart Environments for Health and Well-being (IHSH)

The rapid increase and expansion of cyber-attacks requires the development of new quality tools t... more The rapid increase and expansion of cyber-attacks requires the development of new quality tools to reduce, combat, and eventually stop their risks. In this context, an Intrusion Prevention Systems (IPS) is introduced. It is an extended IDS solutions network security technology characterized by adding the ability to block threats and detect vulnerabilities exploits. Unlike its predecessor, the IPS is placed as an inline security component where it actively processes via analyzing and taking automated actions on all traffic flows that enter the network. Needless to say, speed and efficiency are a necessity in the IPS to avoid degrading network performance. On one hand, signature-based detection and statistical anomaly-based detection, two dominant detection methods mechanisms, are responsible for finding exploits whenever statistical features are extracted to characterize network traffic flows. The computation cost of the classifier, therefore, will be overlarge. On the other hand, the feature selection problem, a critical component in reducing features and improving overall classification accuracy, is about a highly complex NP-hard problem in a Data science. In this paper, a novel intrusion detection system is proposed. It is a double-action system with meta-classifier based feature selection as well as an ensemble learning meta-classifier for stacking via cross-validation to prevent overfitting. Therefore, a better subset of informative features for each type of attacks was selected rather than the features common to all attacks. Finally, this work, through the several experiments, demonstrates that our proposed model not only reaches high detection rates and significantly reduces false alarms, but also accelerates the learning and the testing process thereby directly contributing to the overall ability to work in online mode and scalability.

The Prague Bulletin of Mathematical Linguistics Towards a New Approach for Disambiguation in NLP by Multiple Criterian Decision-Aid

The aim of this paper is to present a combination of NLP and Multiple Criteria Decision-Aid (MCDA... more The aim of this paper is to present a combination of NLP and Multiple Criteria Decision-Aid (MCDA) in order to reach an effective analysis when dealing with linguistic data from various sources. The coexistence of these two concepts has allowed us, based on a set of actions and criteria, to develop a coherent system that integrates the entire process of textual data analysis (no-voweled Arabic texts) into decision making in case of ambiguity. Our solution is based on decision theory and an MCDA approach with a TOPSIS technique. This method allows the multi-scenario classification of morphosyntactical ambiguity cases in order to come out with the best performance and reduce the number of candidate scenarios.

Packing chromatic numbers of finite super subdivisions of graphs

Filomat, 2020

Given a graph G and a positive integer i, an i-packing in G is a subset W of the vertex set of G ... more Given a graph G and a positive integer i, an i-packing in G is a subset W of the vertex set of G such that the distance between any two distinct vertices from W is greater than i. The packing chromatic number of a graph G, ??(G), is the smallest integer k such that the vertex set of G can be partitioned into sets Vi, i ? {1,..., k}, where each Vi is an i-packing. In this paper, we present some general properties of packing chromatic numbers of finite super subdivisions of graphs. We determine the packing chromatic numbers of the finite super subdivisions of complete graphs, cycles and some neighborhood corona graphs.

TAGHIT: Un étiqueteur Morphosyntaxique de l’Arabe Basé sur une Approche Multicritère

Makespan minimization for two-stage hybrid Flow shop with dedicated machines and additional constraints

This paper considers a two-stage hybrid flow shop scheduling problem. The objective is the minimi... more This paper considers a two-stage hybrid flow shop scheduling problem. The objective is the minimizing of maximum completion time of all the jobs. There exist two dedicated machines at stage 1 and one machine at stage 2. Each job is defined by two operations processed on the two-stages in series. Depending on the job type, the job is processed on either of the two machines at stage1 and must be processed on the single machine at stage2. the jobs are transported between the stages by a robot or a conveyor. After the problem formulation, we present lower bounds for the objective function. We then discuss a few polynomially solvable cases of the problem and present the solution algorithms. Since a general case of the problem is strongly NP-hard, we propose two heuristics to find approximate solutions to the general case. Computational experiments are done on a number of randomly generated test problems, and the test results are reported.

On locating chromatic number of Möbius ladder graphs

Proyecciones (Antofagasta), 2021

In this paper, we are dealing with the study of locating chromatic number of Möbius-ladders. We p... more