On the maximum ABC index of graphs without pendent vertices

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

Applied Mathematics and Computation, 2017, vol. 315, issue C, 298-312

Abstract: Let G be a simple graph. The atom–bond connectivity index (ABC) of G is defined as ABC(G)=∑uv∈E(G)d(u)+d(v)−2d(u)d(v), where d(v) denotes the degree of vertex v of G. We characterize the graphs with n vertices, minimum vertex degree ≥ 2, and m edges for m=2n−4 and m=2n−3, that have maximum ABC index.

Keywords: Degree (of vertex); Atom–bond connectivity index; ABC index; Extremal graph (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:315:y:2017:i:c:p:298-312

DOI: 10.1016/j.amc.2017.07.075

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