Extremal pentagonal chains with respect to bond incident degree indices

Ali, Akbar; Raza, Zahid; Bhatti, Akhlaq Ahmad

doi:10.1139/cjc-2016-0308

Cited by 26 publications

(17 citation statements)

References 30 publications

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“…Fig. 2: Carbon graphite graph for (3,4) and t = 3. Table 1: Edge partition of CG(m, n) based on degree sum of end vertices of each edge.…”

Section: R a F T 2 Main Resultsmentioning

confidence: 99%

“…Some applications related to topological indices of molecular graphs are given in 2,3,9,12,13,18,19,23,26,27,28 and also the references therein. The researchers work in the field of chemical graph theory about the topological applications of carbon nanocones, extremal pentagonal chains, tree like polyphenylene, spiro hexagonal systems, polyphenylene dendrimer nanostars, nanostructures, and polyomino chains in 1,[4][5][6]25 . These chemical applications are motivated us to study topological descriptors and compute for some new chemical graphs.…”

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confidence: 99%

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Molecular description of carbon graphite and crystal cubic carbon structures

2017

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Graph theory plays a vital role in modeling and designing any chemical structure or chemical network. Chemical graph theory helps in understanding the molecular structural properties of a molecular graph. The molecular graph consists of atoms called vertices and chemical bonds between atoms called edges. In this article, we study the chemical graphs of carbon graphite and crystal structure of cubic carbon. Moreover, we compute and give closed formulas of degree-based additive topological indices, mainly the first and second Zagreb indexes, general Randić index, atom bond connectivity index, geometric arithmetic index, fourth atom bond connectivity index, and fifth geometric arithmetic index of carbon graphite denoted by CG(m, n) for t levels, and crystal structure cubic carbon denoted for n levels.

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“…Fig. 2: Carbon graphite graph for (3,4) and t = 3. Table 1: Edge partition of CG(m, n) based on degree sum of end vertices of each edge.…”

Section: R a F T 2 Main Resultsmentioning

confidence: 99%

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confidence: 99%

Molecular description of carbon graphite and crystal cubic carbon structures

2017

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“…In fact, there also exist numerous research results for a general pentachain. For example, Xiao et al [45] studied a connection between the Kekulé structures of pentachains and the Hosoya index of caterpillar trees, and a general expression for calculating the bond incident degree indices of pentachains was established in [46]. Denote by E[Ξ] the expected value of a random variable.…”

Section: Introductionmentioning

confidence: 99%

Comparison of the Wiener and Kirchhoff Indices of Random Pentachains

Wei

Shiu

et al. 2021

Journal of Mathematics

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Let G be a connected (molecule) graph. The Wiener index W G and Kirchhoff index K f G of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G , respectively. In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff indices of random pentachains are derived by the difference equation and recursive method. Based on these formulae, we then make comparisons between the expected values of the Wiener index and the Kirchhoff index in random pentachains and present the average values of the Wiener and Kirchhoff indices with respect to the set of all random pentachains with n pentagons.

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“…There are lot of research papers related to the GA index of a graph G which can be found in literature, see for example [9] , [10] , [11] . There are plenty of papers outlined the mathematical properties of these four indices, for example one can consults the papers [10] , [12] , [13] , [14] , [15] , [16] , [17] , [18] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

The expected values of arithmetic bond connectivity and geometric indices in random phenylene chains

Raza

2020

Heliyon

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Phenylenes are a class of conjugated hydrocarbons composed of a special arrangement of six- and four-membered rings. In this paper, the expected values of the atom-bond connectivity (ABC), geometric-arithmetic (GA), and Zagreb indices of this class of conjugated hydrocarbons have been determined. At the end, the comparisons with respect to the random phenylene chains among the expected values of these indices, have been determined explicitly. The graphical profiles of these indices have been shown in order to support our results.

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Extremal pentagonal chains with respect to bond incident degree indices

Cited by 26 publications

References 30 publications

Molecular description of carbon graphite and crystal cubic carbon structures

Molecular description of carbon graphite and crystal cubic carbon structures

Comparison of the Wiener and Kirchhoff Indices of Random Pentachains

The expected values of arithmetic bond connectivity and geometric indices in random phenylene chains

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