On atom-bond connectivity index of graphs

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)di+dj−2didj, where di is the degree of vertex vi in...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-11, Vol.479 (1), p.1099-1114
Main Authors: Hua, Hongbo, Das, Kinkar Chandra, Wang, Hongzhuan
Format: Article
Language:English
Subjects:
ABC-index
Clique number
Diaz-Metcalf inequality
Mycielski graph
Radius
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Summary: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)di+dj−2didj, 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.06.069