Ordering Graphs by the Augmented Zagreb Indices
Received:July 25, 2014  Revised:December 22, 2014
Key Words: augmented Zagreb index   connected graphs   trees   unicyclic graphs   bicyclic graphs  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11326221).
Author NameAffiliation
Yufei HUANG Department of Mathematics Teaching, Guangzhou Civil Aviation College, Guangdong 510403, P. R. China 
Bolian LIU College of Mathematical Science, South China Normal University, Guangdong 510631, P. R. China 
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Abstract:
      Recently, Furtula et al. proposed a valuable predictive index in the study of the heat of formation in octanes and heptanes, the augmented Zagreb index (AZI index) of a graph $G$, which is defined as $$\AZI(G)=\sum_{uv\in E(G)}\big(\frac{d_ud_v}{d_u+d_v-2}\big)^3,$$ where $E(G)$ is the edge set of $G$, $d_u$ and $d_v$ are the degrees of the terminal vertices $u$ and $v$ of edge $uv$, respectively. In this paper, we obtain the first five largest (resp., the first two smallest) AZI indices of connected graphs with $n$ vertices. Moreover, we determine the trees of order $n$ with the first three smallest AZI indices, the unicyclic graphs of order $n$ with the minimum, the second minimum AZI indices, and the bicyclic graphs of order $n$ with the minimum AZI index, respectively.
Citation:
DOI:10.3770/j.issn:2095-2651.2015.02.001
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