Year: 2017
Author: Yufei Huang
Communications in Mathematical Research , Vol. 33 (2017), Iss. 1 : pp. 8–18
Abstract
Let $G$ be a simple connected graph with vertex set $V (G)$ and edge set $E(G)$. The augmented Zagreb index of a graph $G$ is defined as
$$AZI(G)=\sum_{uv\in E(G)}\left(\frac{d_ud_v}{d_u+d_v-2}\right)^3,$$
and the atom-bond connectivity index (ABC index for short) of a graph $G$ is defined as$$ABC(G)=\sum_{uv\in E(G)}\sqrt{\frac{d_u+d_v-2}{d_ud_v}},$$
where $d_u$ and $d_v$ denote the degree of vertices $u$ and $v$ in $G$, respectively. In this paper, trees with given diameter minimizing the augmented Zagreb index and maximizing the ABC index are determined, respectively.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2017.01.02
Communications in Mathematical Research , Vol. 33 (2017), Iss. 1 : pp. 8–18
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: tree augmented Zagreb index ABC index diameter