On atom-bond connectivity index of graphs

Hongbo Hua; Kinkar Chandra Das; Hongzhuan Wang

doi:10.1016/j.jmaa.2019.06.069

On atom-bond connectivity index of graphs

Hongbo Hua, Kinkar Chandra Das, Hongzhuan Wang

Department of Mathematics

Huaiyin Institute of Technology

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

The atom-bond connectivity index (ABC-index) is a useful topological index employed in studying the stability of alkanes and the strain energy of cycloalkanes. The ABC-index of a nontrivial graph G, denoted by ABC(G), is defined as ABC(G)=∑v_iv_j∈E(G)[Formula presented], where d_i is the degree of vertex v_i in G. In this paper, we first present some lower bounds for ABC-index by means of some known inequalities. Then we give some upper bounds for ABC-index in terms of graph parameters such as clique number, vertex connectivity, algebraic connectivity and spectral radius. Moreover, we give some lower and upper bounds for ABC-index of Mycielski graphs. Finally, we compare ABC-index with other graph invariants for connected graphs.

Original language	English
Pages (from-to)	1099-1114
Number of pages	16
Journal	Journal of Mathematical Analysis and Applications
Volume	479
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2019.06.069
State	Published - 1 Nov 2019

Keywords

ABC-index
Clique number
Diaz-Metcalf inequality
Mycielski graph
Radius

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10.1016/j.jmaa.2019.06.069

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title = "On atom-bond connectivity index of graphs",

abstract = "The atom-bond connectivity index (ABC-index) is a useful topological index employed in studying the stability of alkanes and the strain energy of cycloalkanes. The ABC-index of a nontrivial graph G, denoted by ABC(G), is defined as ABC(G)=∑vivj∈E(G)[Formula presented], where di is the degree of vertex vi in G. In this paper, we first present some lower bounds for ABC-index by means of some known inequalities. Then we give some upper bounds for ABC-index in terms of graph parameters such as clique number, vertex connectivity, algebraic connectivity and spectral radius. Moreover, we give some lower and upper bounds for ABC-index of Mycielski graphs. Finally, we compare ABC-index with other graph invariants for connected graphs.",

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T1 - On atom-bond connectivity index of graphs

AU - Hua, Hongbo

AU - Das, Kinkar Chandra

AU - Wang, Hongzhuan

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AB - The atom-bond connectivity index (ABC-index) is a useful topological index employed in studying the stability of alkanes and the strain energy of cycloalkanes. The ABC-index of a nontrivial graph G, denoted by ABC(G), is defined as ABC(G)=∑vivj∈E(G)[Formula presented], where di is the degree of vertex vi in G. In this paper, we first present some lower bounds for ABC-index by means of some known inequalities. Then we give some upper bounds for ABC-index in terms of graph parameters such as clique number, vertex connectivity, algebraic connectivity and spectral radius. Moreover, we give some lower and upper bounds for ABC-index of Mycielski graphs. Finally, we compare ABC-index with other graph invariants for connected graphs.

KW - ABC-index

KW - Clique number

KW - Diaz-Metcalf inequality

KW - Mycielski graph

KW - Radius

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DO - 10.1016/j.jmaa.2019.06.069

M3 - Article

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JF - Journal of Mathematical Analysis and Applications

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On atom-bond connectivity index of graphs

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