Modified Zagreb connection indices of the T-sum graphs

HINDAWI, JOURNAL OF CHEMISTRY, 2019

Representation or coding of the molecular graphs with the help of numerical numbers plays a vital role in the studies of physicochemical and structural properties of the chemical compounds that are involved in the molecular graphs. For the first time, the modified first Zagreb connection index appeared in the paper by Gutman and Trinajstic (1972) to compute total electron energy of the alternant hydrocarbons, but after that, for a long time, it has not been studied. Recently, Ali and Trinajstic (2018) restudied the first Zagreb connection index (ZC 1), the second Zagreb connection index (ZC 2), and the modified first Zagreb connection index (ZC * 1) to find entropy and acentric factor of the octane isomers. ey also reported that the values provided by the International Academy of Mathematical Chemistry show better chemical capability of the Zagreb connection indices than the ordinary Zagreb indices. Assume that S 1 and S 2 denote the operations of subdivision and semitotal point, respectively. en, the S-sum graphs Q 1 + S Q 2 are obtained by the cartesian product of S(Q 1) and Q 2 , where S ∈ S 1 , S 2 , Q 1 and Q 2 are any connected graphs, and S(Q 1) is a graph obtained after applying the operation S on Q 1. In this paper, we compute the Zagreb connection indices (ZC 1 , ZC 2 , and ZC * 1) of the S-sum graphs in terms of various topological indices of their factor graphs. At the end, as an application of the computed results, the Zagreb connection indices of the S-sum graphs obtained by the particular classes of alkanes are also included.

Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015), 2016

The atom bond connectivity (ABC) index is one of the recently most investigated degree-based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as ABCðGÞ ¼ P uv2EðGÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi d v þ d u À 2=d v Á d u p , where d u denotes the degree of a vertex u in G. In this paper, we obtain the general formula for ABC index of some special, chemical trees, and bicyclic graphs. Keywords The atom bond connectivity (ABC) index Á Bicyclic graphs Á Molecular graphs Á Chemical tree 27.1 Introduction Molecular descriptors have found a wide application in quantitative structureactivity relationship analysis (QSAR) and in quantitative structure-property relationship (QSPR) (targets the estimation of specific characteristics based on the structures of the compounds under study) studies [10]. Among them, topological

Journal of Physical & Theoretical Chemistry, 2015

It is well known that the chemical behavior of a compound is dependent upon the structure of its molecules. Quantitative structure -activity relationship (QSAR) studies and quantitative structureproperty relationship (QSPR) studies are active areas of chemical research that focus on the nature of this dependency. Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indices for examination of structure-property relationship is Randic' index. In this study is represented the relationship between the Randic', Balaban and Szeged indices and Harary numbers to the octanol-water partition coefficient (logP) of monocarboxylic acids (C 2 -C 20 ) are established, and then, some useful topological indices for examination of the structure-property relationship are presented.

2020

A graph is a mathematical model used to predict the topology of a given system. In chemical graph theory, a graph is designed by considering atoms as vertices and edges as bonds between atoms of a particular molecule. A topological index or molecular structure descriptor is a numeric quantity associated with the chemical constitution which correlated with various physiochemical properties of the chemical structure. In this paper, we study the [Formula: see text]-Zagreb index of line graphs of the subdivision graphs of some chemical structures.

Journal of Chemical Information and Modeling, 1998

The concept of edge connectivity index is extended to a series of indices based on adjacency between edges in various fragments of the molecular graph. The analogous concept of vertex adjacency indices of the line graph of the molecular graph is also introduced. Some mathematical relations between both series of indices are found, showing that line-graph-based connectivity indices are linear combinations of edge-based descriptors. The study of eight representative physical properties of alkanes was used to compare the ability of both series of indices to produce significant quantitative structure-property relationship (QSPR) models.

Journal of Physical & Theoretical Chemistry, 2007

The fact that the properties of a molecule are tightly connected to its structural characteristics is one of the fundamental concepts in chemistry. In this connection, graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. So , a novel method for computing the new descriptors to construct a quantitative relation between structure and properties is presented. At first, a brief review on the classical graph theories introduced and, then, the link with molecular similarity is drawn. In the applications section, molecular topological indices are calculated. Afterwards, the molecular descriptors, that include the necessary structural information for properly describtion of system are employed to derive a numerical correlation with thermodynamic properties. Finally, some useful topological indices for examination of the structure-property relationship are presented. In addition, the relationship between the Randic / , Wiener, Hosoya , Balaban and Schultz indices and Harary numbers and Distance matrix to the enthalpies of formation ( ) f o H ∆ , heat capacities, (Cp) , enthalpies of combustion ( ) c o H ∆ , enthalpies of vaporization ( ) vap H o ∆ and normal boiling points ( ) bpK for 10 2 C Cnormal alcohols is established.

Journal of Molecular Structure-theochem, 1997

Atoms, 2019

Topological index is an invariant of molecular graphs which correlates the structure with different physical and chemical invariants of the compound like boiling point, chemical reactivity, stability, Kovat’s constant etc. Eccentricity-based topological indices, like eccentric connectivity index, connective eccentric index, first Zagreb eccentricity index, and second Zagreb eccentricity index were analyzed and computed for families of Dutch windmill graphs and circulant graphs.

Complex., 2021

The study of structure-property relations including the transformations of molecules is of utmost importance in correlations with corresponding physicochemical properties. The graph topological indices have been used effectively for such study and, in particular, bond-based indices play a vital role. The bond-additive topological indices of a molecular graph are defined as a sum of edge measures over all edges in which edge measures can be computed based on degrees, closeness, peripherality, and irregularity. In this study, we provide the mathematical characterization of the transformation of a structure that can be accomplished by the novel edge adjacency and incidence relations. We derive the exact expressions of bond type indices such as second Zagreb, sigma indices, and their coindices of total transformation and two types of semitransformations of the molecules which in turn can be used to characterize the topochemical and topostructural properties.

Journal of Chemistry

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. Topological indices help us collect information about algebraic graphs and give us mathematical approach to understand the properties of algebraic structures. With the help of topological indices, we can guess the properties of chemical compounds without performing experiments in wet lab. There are more than 148 topological indices in the literature, but none of them completely give all properties of under study compounds. Together, they do it to some extent; hence, there is always room to introduce new indices. In this paper, we present first and second reserve Zagreb indices and first reverse hyper-Zagreb indices, reverse GA index, and reverse atomic bond connectivity index for the crystallographic structure of molecules. We also present first and second reverse Zagreb polynomials and first and second reverse hyper-Zagreb polyn...

Three vertex-degree-based graph invariants are presented, that earlier have been considered in the chemical and/or mathematical literature, but that evaded the attention of most mathematical chemists. These are the reciprocal Randić index (RR), the reduced second Zagreb index RM 2 , and the reduced reciprocal Randić index (RRR). If d 1 , d 2 , . . . , d n are the degrees of the vertices of the graph G = (V, E), then

Journal of Chemistry, 2019

Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p∈VΓdΓp2 and ∏1Γ=∏pq∈EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq∈EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479–-105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the f...

Journal of Chemical Information and Modeling, 2007

The sequence of all paths p i of lengths i) 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Σ i p i 2 , and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q) Σ i p i 2 /(µ+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Σ i p i 1/2 , and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S) Σ i p i 1/2 /(µ+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D) Σ i {p i 1/2 /[i(µ+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A) Σ i {p i /[i(µ + 1)]}; and (v) the last TI with two square roots: Path-count index: P) Σ i {p i 1/2 / [i 1/2 (µ + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property. † Dedicated to Professor Nenad Trinajstić on the occasion of his 70th birthday.

Combinatorial Chemistry & High Throughput Screening,, 2023

Background: Chemical graph theory has been used to mathematically model the various physical and biological aspects of chemical substances. A mathematical formulation that may be applied to any graph and can characterise a molecule structure is known as a topological index or molecular descriptor. Method: It is convenient and efficient to analyse the mathematical values and further research on various physical properties of a molecule based on these molecular descriptors. They provide useful alternatives to lengthy, expensive, and labour-intensive laboratory experiments. The topological indices can be used to predict the chemical structures, physicochemical properties, and biological activities using quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs). Result: In this study, the molecular descriptors of the Dodeca-benzo-circumcorenene compounds are derived based on their corresponding molecular structures. Conclusion: The computed indices are then compared graphically to study their relationship with the molecular structure and with each other.

Chemical Physics Letters, 2004

Based on chemical signed graph theory proposed by Lee et al. the novel information theoretic topological index, I k , is derived from the edge signed graphs. Subsequently, based on the definition of I k , few other properties based information theoretic indices such as, bonding information index, I b , non-bonding information index, I n , and anti-bonding information index, I a , are also evaluated. Moreover, the index, I b and I a are found to be useful in QSAR modeling of unsaturated hydrocarbons.