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arXiv · 2304.06241

The extremal unicyclic graphs of the revised edge Szeged index with given diameter

Shengjie He·Qiaozhi Geng·Rong-Xia Hao
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Abstract

Let $G$ be a connected graph. The revised edge Szeged index of $G$ is defined as $Sz^{\ast}_{e}(G)=\sum\limits_{e=uv\in E(G)}(m_{u}(e|G)+\frac{m_{0}(e|G)}{2})(m_{v}(e|G)+\frac{m_{0}(e|G)}{2})$, where $m_{u}(e|G)$ (resp., $m_{v}(e|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), and $m_{0}(e|G)$ is the number of edges equidistant from both ends of $e$, respectively. In this paper, the graphs with minimum revised edge Szeged index among all the unicyclic graphs with given diameter are characterized.

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Shengjie He, Qiaozhi Geng, Rong-Xia Hao. 2023-04-13. The extremal unicyclic graphs of the revised edge Szeged index with given diameter. https://arxiv.org/abs/2304.06241

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