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
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Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11326221). |
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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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