On the maximum ABC index of graphs without pendent vertices

Shao, Zehui; Wu, Pu; Gao, Yingying; Gutman, Ivan; Zhang, Xiujun

doi:10.1016/j.amc.2017.07.075

Cited by 89 publications

(40 citation statements)

References 16 publications

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“…The ABC index provides a very good correlation for the stability of linear alkanes as well as the branched alkanes and for computing the strain energy of cyclo alkanes [17][18][19][20]. To correlate with certain physico-chemical properties, the GA index has much better predictive power than the predictive power of the Randic connectivity index [21][22][23]. The first and second Zagreb index were found to occur for computation of the total π-electron energy of the molecules within specific approximate expressions [24].…”

Section: Applications Of Topological Indices and Motivationmentioning

confidence: 99%

Eccentricity Based Topological Indices of an Oxide Network

et al. 2018

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Graph theory has much great advances in the field of mathematical chemistry. Chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. A great variety of such indices are studied and used in theoretical chemistry, pharmaceutical researchers, in drugs and in different other fields. In this article, we study the chemical graph of an oxide network and compute the total eccentricity, average eccentricity, eccentricity based Zagreb indices, atom-bond connectivity (ABC) index and geometric arithmetic index of an oxide network. Furthermore, we give analytically closed formulas of these indices which are helpful in studying the underlying topologies.

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Section: Applications Of Topological Indices and Motivationmentioning

confidence: 99%

Eccentricity Based Topological Indices of an Oxide Network

et al. 2018

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“…For example, the Wiener index [13] and the Balaban J index [14] are based on the distance of vertices in the respective graph, the Estrada index, [15] and the energy of a graph. [17,18] Graph theory has provided theoretical chemists with a variety of useful tools, such as topological matrices, topological polynomials, and topological indices. [17,18] Graph theory has provided theoretical chemists with a variety of useful tools, such as topological matrices, topological polynomials, and topological indices.…”

Section: Introductionmentioning

confidence: 99%

“…The theory of chemical graphs is a branch of mathematical chemistry, in fact, graph theory is connectivity between chemistry and mathematics, and solves many of the difficult problems of mathematical chemistry using graph theory, for more details you can see References [1-3] The topologic index is known as a connection index, in fact, the topology index describes the chemical composition based on the molecular structure. [17,18] Graph theory has provided theoretical chemists with a variety of useful tools, such as topological matrices, topological polynomials, and topological indices. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure.…”

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confidence: 99%

On topological indices of carbon nanocones and nanotori

Jahanbani

2019

Int J of Quantum Chemistry

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Let G be a graph with n vertices and d i is the degree of its ith vertex (d i is the degree of v i ). In this article, we compute the redefined first Zagreb index, redefined second Zagreb index, redefined third Zagreb index, augmented Zagreb index of graphs carbon nanocones CNC k [n], and nanotori [C 4 C 6 C 8 (p,q)]. Also, compute the multiplicative redefined first Zagreb index, multiplicative redefined second Zagreb index, multiplicative redefined third Zagreb index, multiplicative augmented Zagreb index of carbon nanocones CNC k [n], and nanotori [C 4 C 6 C 8 (p,q)]. K E Y W O R D Saugmented Zagreb index, carbon nanocones, nanotori, re-defined Zagreb index, topological index 1 | INTRODUCTION Mathematical chemistry is a branch of theoretical chemistry that investigate the molecular structure using graph theory. In other words, by specifies the vertices, edges, and degree vertices graph of the molecular structure, it certain the properties of the chemistry of this structure using mathematical methods. These methods solve many of the problems of chemistry. The theory of chemical graphs is a branch of mathematical chemistry, in fact, graph theory is connectivity between chemistry and mathematics, and solves many of the difficult problems of mathematical chemistry using graph theory, for more details you can see References [1-3] The topologic index is known as a connection index, in fact, the topology index describes the chemical composition based on the molecular structure. [4][5][6] Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. [7] Writing the mathematical model of a problem in various science is a helpful tool which helps a great deal to their progress. As an example, a graph can be drawn in chemistry based on atoms and the existing bonds between them for every molecule and the graph mathematical models can be defined in order to analyze the molecule. Topological indices are one of the mathematical models that can be defined by assigning a real number to the chemical molecule.Topological indices of large chemical structures such as metal organic frameworks can be extremely useful in both characterization of structures and computing their physicochemical properties that are otherwise difficult to compute for such large networks of importance in reticular chemistry. Synthesis of novel reticular metal-organic frameworks and networks in which covalent fibers are weaved into crystals are becoming increasingly important in recent years. [8,9] Topological indices numerically represent the structural characteristics of molecules that are obtained by the use of graph-theoretical concepts applied to these large networks of interest in reticular chemistry. In addition, the mathematical techniques comprising of group theory a...

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“…The Randic index is a topological descriptor related to a great deal of synthetic qualities of atoms and was discovered parallel to processing the boiling point and Kovats constants of the particles. The particle bond network ( ) index connects to the security of direct alkanes and stretched alkanes and is used to process the strain vitality of cycloalkanes [38,39]. In terms of physicoconcoction properties, the index has prescient control superior to the prescient energy of the Randic connectivity index [40].…”

Section: Applications Of Topological Indicesmentioning

confidence: 99%

On Topological Indices of Fractal and Cayley Tree Type Dendrimers

Imran

Baig

Khalid

2018

Discrete Dynamics in Nature and Society

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The topological descriptors are the numerical invariants associated with a chemical graph and are helpful in predicting their bioactivity and physiochemical properties. These descriptors are studied and used in mathematical chemistry, medicines, and drugs designs and in other areas of applied sciences. In this paper, we study the two chemical trees, namely, the fractal tree and Cayley tree. We also compute their topological indices based on degree concept. These indices include atom bond connectivity index, geometric arithmetic index and their fourth and fifth versions, Sanskruti index, augmented Zagreb index, first and second Zagreb indices, and general Randic index for = {−1, 1, 1/2, −1/2}. Furthermore, we give closed analytical results of these indices for fractal trees and Cayley trees.

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On the maximum ABC index of graphs without pendent vertices

Cited by 89 publications

References 16 publications

Eccentricity Based Topological Indices of an Oxide Network

Eccentricity Based Topological Indices of an Oxide Network

On topological indices of carbon nanocones and nanotori

On Topological Indices of Fractal and Cayley Tree Type Dendrimers

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