INTERNATIONAL JOURNAL OF MULTIDISCIPLINARY RESEARCH AND ANALYSIS, 2022
Networks play an important role in electrical and electronic engineering. It depends on what area... more Networks play an important role in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example, there is a lot more abstract mathematics in communication theory and signal processing and networking, etc. Networks involve nodes communicating with each other. Graph theory has found considerable use in this area. In this paper, we introduce some new Networks such as Graph-PW, Network Symmetric Digraph-PW, Change Network Graph-PW, and Change Network Symmetric Digraph-PW. Moreover, several theorems and results of these networks have been studied.
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
In this paper, we introduce Zagreb Indices of Some New Graphs. Exactly, first index, second index... more In this paper, we introduce Zagreb Indices of Some New Graphs. Exactly, first index, second index and forgotten index. New graphs are generated from the initial graphs by graph operations. We also created some possible applications on the Zagreb indices as special cases.
In this paper, we introduce new binary operations on graphs. In fact, we obtained some other prod... more In this paper, we introduce new binary operations on graphs. In fact, we obtained some other product operations, called them classic product operations from union of two or more new product operations. We examined the relationship between new binary product operations and classic product operations.
Let G and H be two graphs and G c and H c their complement respectively. We define new operation ... more Let G and H be two graphs and G c and H c their complement respectively. We define new operation on graphs, called semi-complete product and denoted by. where G H = (G ∨ H) ∪ (G c × H c). In this paper, we compute some topological indices of G H, such as Wiener index, Hyper-Wiener index, Wiener polarity, Schultz index, Gutman index and other relationship.
This paper is devoted to the study of a new graph, called m k-graph and denoted by m k ðGÞ, that ... more This paper is devoted to the study of a new graph, called m k-graph and denoted by m k ðGÞ, that arises from a simple graph G by k successive iterations of a special kind of construction. We provide some of its topological indices such as Wiener index, Hyper-Wiener index, Wiener polarity, Zagreb indices, Schultz and modified Schultz indices and Wiener-type invariant. Some Formulas concerning classical graphs are settled to show the scope of this study.
A topological index of graph G is a numerical parameter related to graph which characterizes its ... more A topological index of graph G is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join G 1 + G 2 , tensor product G 1 ⊗ G 2 , Cartesian product G 1 × G 2 , composition G 1 • G 2 , strong product G 1 * G 2 , disjunction G 1 ∨ G 2 and symmetric difference G 1 ⊕ G 2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.
A topological index of graph G is a numerical parameter related to G which characterizes its topo... more A topological index of graph G is a numerical parameter related to G which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this paper, we compute some topological indices such as Zagreb indices, Hyper Zagreb indices and Redefined Zagreb indices of conical graphs G(m, n). Moreover we compute the correlation coefficients between them.
The methods on topological index and topological coindex computation are very suitable and servic... more The methods on topological index and topological coindex computation are very suitable and serviceable for developing countries in which they can yield available medical information about new drugs without chemical experiment. For example, in quantitative structure-activity relationships (QSAR) modelling, the predictors consist of theoretical molecular descriptors of chemicals, while the (QSAR) response-variable could be a biological, pharmacological, medical, ecological activity of the chemicals. Recently, proposed new invariant of this kind is the Y-index defined as: YðGÞ ¼ P u2VðGÞ d 4 G ðuÞ ¼ P uv2EðGÞ ½d 3 G ðuÞ þ d 3 G ðvÞ; In this paper, the basic relations between this index and its coindex for a graph G and its complement Gare determined. We compare this new coindex with the other well-known and most used topological indices and coindices in literature by modelling some physicochemical properties of octane isomers. We will find that, the Y-coindex give better correlation than others. Also, we explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations.
Topological indices have important role in theoretical chemistry. Among the all topological indic... more Topological indices have important role in theoretical chemistry. Among the all topological indices the Zagreb indices have been used more considerably than any other topological indices in chemical literature. In this study, the Y-index for some special graphs, and graph operations has been computed, that have been applied to compute the Y-index for Nano-tube and Nano-torus. Also the strong/good correlation coefficient between the Y-index and some physical and chemical properties as Acentric factor (Acenfac), Entropy (S),Enthalpy of vaporization (HVAP) and Standard enthalpy of vaporisation (DHVAP) have been Appeared.
In this study, the Hyper-Zagreb index for some complement graphs operations has been computed, th... more In this study, the Hyper-Zagreb index for some complement graphs operations has been computed, that have been applied to compute the Hyper-Zagreb index for complement molecular graph of a nanotorus and titania nanotubes.
Topological indices have important role in theoretical chemistry. Among the Wiener index has been... more Topological indices have important role in theoretical chemistry. Among the Wiener index has been used more considerably than any other topological indices in chemical literature. In this study, we introduce a new graphs called conical graphs G(m, n) that generalizes the classic wheel graphs.The Wiener polynomial of G(m, n) has been computed. We present explicit formulae for the Wiener index of G(m, n) by considering the cases ⌈ n 4 ⌉ ≤ m and ⌈ n 4 ⌉ > m.
A topological index of graph G is a numerical parameter related to graph which characterizes its ... more A topological index of graph G is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join G 1 + G 2 , tensor product G 1 ⊗ G 2 , Cartesian product G 1 × G 2 , composition G 1 • G 2 , strong product G 1 * G 2 , disjunction G 1 ∨ G 2 and symmetric difference G 1 ⊕ G 2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.
In this paper, some basic mathematical operation for the second Zagreb indices of graph containin... more In this paper, some basic mathematical operation for the second Zagreb indices of graph containing the join and strong product of graph operation, and the first and second Zagreb indices of complement graph operations such as cartesian product G1 × G2, composition G1 • G2, disjunction G1 ∨ G2, symmetric difference G1 ⊕ G2, join G1 + G2, tensor product G1 ⊗ G2, and strong product G1 * G2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.
A topological index is a numerical descriptor of a molecule, based on a certain topological featu... more A topological index is a numerical descriptor of a molecule, based on a certain topological feature of the corresponding molecular graph. In this paper some basic mathematical operation for the hyper Zagreb coindices of graph containing the tensor product G 1 ⊗ G 2 , join G 1 + G 2 , strong product G 1 * G 2 , disjunction G 1 ∨ G 2 and symmetric difference G 1 ⊕G 2 will be explained. Moreover we studied the expression for the hyper-Zagreb coindex of titania TiO 2 [n, m] nanotubes and molecular graph of nanotorus have been derived. These explicit formulae can correlate the chemical structure of titania nanotubes and molecular graph of nanotorus to information about their physical structure.
A chemical graph theory is a fascinating branch of graph theory which has many applications relat... more A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It's found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.
In chemical graph theory, a topological descriptor is a numerical quantity that is based on the c... more In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 ⊗ G2, Cartesian product G1 × G2, composition G1 • G2, strong product G1 * G2, disjunction G1 ∨ G2 and symmetric difference G1 ⊕ G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V P HX[q, p], V-Phenylenic Nanotorus V P HY [m, n] and Titania Nanotubes T iO2.
Topological indices are real numbers related to graphs, They have many applications as tools for ... more Topological indices are real numbers related to graphs, They have many applications as tools for modeling chemical and other properties of molecules. In this paper, we study new graphs called Spider's web graph. Wiener index, Hyper-Wiener index, Wiener polarity and the Schultz indices of Spider's web graph have been computed. Furthermore, we found the correlation between these topological indices of Spider's web graph by some statistical parameters.
A graph can be recognized by numeric number, polynomial or matrix which represent the whole graph... more A graph can be recognized by numeric number, polynomial or matrix which represent the whole graph. Topological index is a numerical descriptor of a molecule, based on a certain topological feature of the corresponding molecular graph, it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. Zagreb indices are numeric numbers related to graphs. In this study, the second Hyper-Zagreb index for some special graphs, and graph operations has been computed, that have been applied to compute the second Hyper-Zagreb index for Nano-tube and Nano-torus.
The forgotten topological index was defined to be used in the analysis of chemical structures whi... more The forgotten topological index was defined to be used in the analysis of chemical structures which often appear in drug molecular graphs. In this paper, we studied the F-index and F-coindex for certain important physico chemical structures such as V-Phenylenic Nanotube V P HX[m, n] and V-Phenylenic Nanotorus V P HY [m, n] and their molecular complement graph. Moreover, we computed F-polynomial of the V-Phenylenic Nanotubes and Nanotorus. These explicit formulae can correlate the chemical structure of molecular graphs of Nanotubes and Nanotorus to information about their physicochemical structure.
INTERNATIONAL JOURNAL OF MULTIDISCIPLINARY RESEARCH AND ANALYSIS, 2022
Networks play an important role in electrical and electronic engineering. It depends on what area... more Networks play an important role in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example, there is a lot more abstract mathematics in communication theory and signal processing and networking, etc. Networks involve nodes communicating with each other. Graph theory has found considerable use in this area. In this paper, we introduce some new Networks such as Graph-PW, Network Symmetric Digraph-PW, Change Network Graph-PW, and Change Network Symmetric Digraph-PW. Moreover, several theorems and results of these networks have been studied.
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
In this paper, we introduce Zagreb Indices of Some New Graphs. Exactly, first index, second index... more In this paper, we introduce Zagreb Indices of Some New Graphs. Exactly, first index, second index and forgotten index. New graphs are generated from the initial graphs by graph operations. We also created some possible applications on the Zagreb indices as special cases.
In this paper, we introduce new binary operations on graphs. In fact, we obtained some other prod... more In this paper, we introduce new binary operations on graphs. In fact, we obtained some other product operations, called them classic product operations from union of two or more new product operations. We examined the relationship between new binary product operations and classic product operations.
Let G and H be two graphs and G c and H c their complement respectively. We define new operation ... more Let G and H be two graphs and G c and H c their complement respectively. We define new operation on graphs, called semi-complete product and denoted by. where G H = (G ∨ H) ∪ (G c × H c). In this paper, we compute some topological indices of G H, such as Wiener index, Hyper-Wiener index, Wiener polarity, Schultz index, Gutman index and other relationship.
This paper is devoted to the study of a new graph, called m k-graph and denoted by m k ðGÞ, that ... more This paper is devoted to the study of a new graph, called m k-graph and denoted by m k ðGÞ, that arises from a simple graph G by k successive iterations of a special kind of construction. We provide some of its topological indices such as Wiener index, Hyper-Wiener index, Wiener polarity, Zagreb indices, Schultz and modified Schultz indices and Wiener-type invariant. Some Formulas concerning classical graphs are settled to show the scope of this study.
A topological index of graph G is a numerical parameter related to graph which characterizes its ... more A topological index of graph G is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join G 1 + G 2 , tensor product G 1 ⊗ G 2 , Cartesian product G 1 × G 2 , composition G 1 • G 2 , strong product G 1 * G 2 , disjunction G 1 ∨ G 2 and symmetric difference G 1 ⊕ G 2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.
A topological index of graph G is a numerical parameter related to G which characterizes its topo... more A topological index of graph G is a numerical parameter related to G which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this paper, we compute some topological indices such as Zagreb indices, Hyper Zagreb indices and Redefined Zagreb indices of conical graphs G(m, n). Moreover we compute the correlation coefficients between them.
The methods on topological index and topological coindex computation are very suitable and servic... more The methods on topological index and topological coindex computation are very suitable and serviceable for developing countries in which they can yield available medical information about new drugs without chemical experiment. For example, in quantitative structure-activity relationships (QSAR) modelling, the predictors consist of theoretical molecular descriptors of chemicals, while the (QSAR) response-variable could be a biological, pharmacological, medical, ecological activity of the chemicals. Recently, proposed new invariant of this kind is the Y-index defined as: YðGÞ ¼ P u2VðGÞ d 4 G ðuÞ ¼ P uv2EðGÞ ½d 3 G ðuÞ þ d 3 G ðvÞ; In this paper, the basic relations between this index and its coindex for a graph G and its complement Gare determined. We compare this new coindex with the other well-known and most used topological indices and coindices in literature by modelling some physicochemical properties of octane isomers. We will find that, the Y-coindex give better correlation than others. Also, we explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations.
Topological indices have important role in theoretical chemistry. Among the all topological indic... more Topological indices have important role in theoretical chemistry. Among the all topological indices the Zagreb indices have been used more considerably than any other topological indices in chemical literature. In this study, the Y-index for some special graphs, and graph operations has been computed, that have been applied to compute the Y-index for Nano-tube and Nano-torus. Also the strong/good correlation coefficient between the Y-index and some physical and chemical properties as Acentric factor (Acenfac), Entropy (S),Enthalpy of vaporization (HVAP) and Standard enthalpy of vaporisation (DHVAP) have been Appeared.
In this study, the Hyper-Zagreb index for some complement graphs operations has been computed, th... more In this study, the Hyper-Zagreb index for some complement graphs operations has been computed, that have been applied to compute the Hyper-Zagreb index for complement molecular graph of a nanotorus and titania nanotubes.
Topological indices have important role in theoretical chemistry. Among the Wiener index has been... more Topological indices have important role in theoretical chemistry. Among the Wiener index has been used more considerably than any other topological indices in chemical literature. In this study, we introduce a new graphs called conical graphs G(m, n) that generalizes the classic wheel graphs.The Wiener polynomial of G(m, n) has been computed. We present explicit formulae for the Wiener index of G(m, n) by considering the cases ⌈ n 4 ⌉ ≤ m and ⌈ n 4 ⌉ > m.
A topological index of graph G is a numerical parameter related to graph which characterizes its ... more A topological index of graph G is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join G 1 + G 2 , tensor product G 1 ⊗ G 2 , Cartesian product G 1 × G 2 , composition G 1 • G 2 , strong product G 1 * G 2 , disjunction G 1 ∨ G 2 and symmetric difference G 1 ⊕ G 2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.
In this paper, some basic mathematical operation for the second Zagreb indices of graph containin... more In this paper, some basic mathematical operation for the second Zagreb indices of graph containing the join and strong product of graph operation, and the first and second Zagreb indices of complement graph operations such as cartesian product G1 × G2, composition G1 • G2, disjunction G1 ∨ G2, symmetric difference G1 ⊕ G2, join G1 + G2, tensor product G1 ⊗ G2, and strong product G1 * G2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.
A topological index is a numerical descriptor of a molecule, based on a certain topological featu... more A topological index is a numerical descriptor of a molecule, based on a certain topological feature of the corresponding molecular graph. In this paper some basic mathematical operation for the hyper Zagreb coindices of graph containing the tensor product G 1 ⊗ G 2 , join G 1 + G 2 , strong product G 1 * G 2 , disjunction G 1 ∨ G 2 and symmetric difference G 1 ⊕G 2 will be explained. Moreover we studied the expression for the hyper-Zagreb coindex of titania TiO 2 [n, m] nanotubes and molecular graph of nanotorus have been derived. These explicit formulae can correlate the chemical structure of titania nanotubes and molecular graph of nanotorus to information about their physical structure.
A chemical graph theory is a fascinating branch of graph theory which has many applications relat... more A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It's found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.
In chemical graph theory, a topological descriptor is a numerical quantity that is based on the c... more In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 ⊗ G2, Cartesian product G1 × G2, composition G1 • G2, strong product G1 * G2, disjunction G1 ∨ G2 and symmetric difference G1 ⊕ G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V P HX[q, p], V-Phenylenic Nanotorus V P HY [m, n] and Titania Nanotubes T iO2.
Topological indices are real numbers related to graphs, They have many applications as tools for ... more Topological indices are real numbers related to graphs, They have many applications as tools for modeling chemical and other properties of molecules. In this paper, we study new graphs called Spider's web graph. Wiener index, Hyper-Wiener index, Wiener polarity and the Schultz indices of Spider's web graph have been computed. Furthermore, we found the correlation between these topological indices of Spider's web graph by some statistical parameters.
A graph can be recognized by numeric number, polynomial or matrix which represent the whole graph... more A graph can be recognized by numeric number, polynomial or matrix which represent the whole graph. Topological index is a numerical descriptor of a molecule, based on a certain topological feature of the corresponding molecular graph, it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. Zagreb indices are numeric numbers related to graphs. In this study, the second Hyper-Zagreb index for some special graphs, and graph operations has been computed, that have been applied to compute the second Hyper-Zagreb index for Nano-tube and Nano-torus.
The forgotten topological index was defined to be used in the analysis of chemical structures whi... more The forgotten topological index was defined to be used in the analysis of chemical structures which often appear in drug molecular graphs. In this paper, we studied the F-index and F-coindex for certain important physico chemical structures such as V-Phenylenic Nanotube V P HX[m, n] and V-Phenylenic Nanotorus V P HY [m, n] and their molecular complement graph. Moreover, we computed F-polynomial of the V-Phenylenic Nanotubes and Nanotorus. These explicit formulae can correlate the chemical structure of molecular graphs of Nanotubes and Nanotorus to information about their physicochemical structure.
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