Maximum values of atom–bond connectivity index in the class of tetracyclic graphs

Dehghan-Zadeh, T.; Ashrafi, Ali Reza; Habibi, Nader

doi:10.1007/s12190-013-0749-y

Cited by 13 publications

(13 citation statements)

References 10 publications

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“…They also determined the n vertex unicyclic graphs with the maximum, the second, the third and the fourth maximum ABC indices, and the n vertex bicyclic graphs, n ≥ 5, with the maximum and the second maximum ABC indices, respectively. The present authors [5], characterized tetracyclic graphs with the maximum and second maximum ABC index.…”

Section: Introductionmentioning

confidence: 90%

Extremal Atom-Bond Connectivity Index of Cactus Graphs

Ашрафи¹,

Dehghan-Zadeh²,

Habibi³

2015

Communications of the Korean Mathematical Society

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Section: Introductionmentioning

confidence: 90%

Extremal Atom-Bond Connectivity Index of Cactus Graphs

Ашрафи¹,

Dehghan-Zadeh²,

Habibi³

2015

Communications of the Korean Mathematical Society

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“…According to Gutman, “the Randić index is the most investigated, most often applied, and most popular among all topological indices. Hundreds of papers and a few books are devoted to this topological index.” Details about the chemical applicability and mathematical properties of this index can be found in the surveys, recent papers, and/or related references cited therein.…”

Section: Introductionmentioning

confidence: 99%

“…Hundreds of papers and a few books are devoted to this topological index. "Details about the chemical applicability and mathematical properties of this index can be found in the surveys, [7,8] recent papers, [9][10][11] and/or related references cited therein.In 1998, Estrada et al [12] devised the following modified version of the Randić index [and called it as atom-bond connectivity (ABC) index]:for predicting the heats of formation of alkanes. Due to chemical applicability of the ABC index, [12][13][14] numerous publications concerning mathematical properties of this index (particularly, related to the characterization of the tree(s) with minimum ABC index among all n-vertex trees) have been and are being appeared, see for example, the surveys, [7,15] recent papers, [16][17][18][19] and/or related references cited therein.…”

mentioning

confidence: 99%

On the difference between atom‐bond connectivity index and Randić index of binary and chemical trees

Ali

2017

Int J of Quantum Chemistry

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This article is devoted to establishing some extremal results with respect to the difference of two well‐known bond incident degree indices [atom‐bond connectivity (ABC) index and Randić (R) index] for the chemical graphs representing alkanes. More precisely, the first three extremal trees with respect to ABC – R are characterized among all n‐vertex binary trees (the trees with maximum degree at most 3). The n‐vertex chemical trees (the trees with maximum degree at most 4) having the first three maximum ABC – R values are also determined.

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“…The aim of this paper is to continue our earlier paper [7] by computing the maximum values of ABC index in the class of all n-vertex tricyclic graphs, TrG(n). According to the terminology of [16],…”

mentioning

confidence: 99%

“…They also shown that the eccentric connectivity index grows at most polynomially with the number of vertices and determined the leading coefficient in the asymptotic behavior. In [7], some of the present authors computed the first and second maximum values of the atom-bond connectivity index in the class of all n-vertex tetracyclic graphs. Fath-Tabar et al [10] obtained some inequalities for this graph invariant under some graph operations.…”

mentioning

confidence: 99%