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Trees with Given Diameter Minimizing the Augmented Zagreb Index and Maximizing the ABC Index

Trees with Given Diameter Minimizing the Augmented Zagreb Index and Maximizing the ABC Index

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

Author Details

Yufei Huang