Volume 33, Issue 1
Trees with Given Diameter Minimizing the Augmented Zagreb Index and Maximizing the ABC Index

Commun. Math. Res., 33 (2017), pp. 8-18.

Published online: 2019-12

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• 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.

• Keywords

tree, augmented Zagreb index, ABC index, diameter

05C35, 05C50

fayger@qq.com (Yufei Huang)

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@Article{CMR-33-8, author = {Yufei and Huang and fayger@qq.com and 5561 and Department of Mathematics Teaching, Guangzhou Civil Aviation College, Guangzhou, 510403 and Yufei Huang}, title = {Trees with Given Diameter Minimizing the Augmented Zagreb Index and Maximizing the ABC Index}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {33}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2017.01.02}, url = {http://global-sci.org/intro/article_detail/cmr/13441.html} }
TY - JOUR T1 - Trees with Given Diameter Minimizing the Augmented Zagreb Index and Maximizing the ABC Index AU - Huang , Yufei JO - Communications in Mathematical Research VL - 1 SP - 8 EP - 18 PY - 2019 DA - 2019/12 SN - 33 DO - http://doi.org/10.13447/j.1674-5647.2017.01.02 UR - https://global-sci.org/intro/article_detail/cmr/13441.html KW - tree, augmented Zagreb index, ABC index, diameter AB -

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.

Yufei Huang. (2019). Trees with Given Diameter Minimizing the Augmented Zagreb Index and Maximizing the ABC Index. Communications in Mathematical Research . 33 (1). 8-18. doi:10.13447/j.1674-5647.2017.01.02
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