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On extremal cacti with respect to the edge revised Szeged index

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 نشر من قبل Shengjie He
 تاريخ النشر 2018
  مجال البحث
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Let $G$ be a connected graph. The edge revised Szeged index of $G$ is defined as $Sz^{ast}_{e}(G)=sumlimits_{e=uvin E(G)}(m_{u}(e|G)+frac{m_{0}(e|G)}{2})(m_{v}(e|G)+frac{m_{0}(e|G)}{2})$, 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 $e$. In this paper, we give the minimal and the second minimal edge revised Szeged index of cacti with order $n$ and $k$ cycles, and all the graphs that achieve the minimal and second minimal edge revised Szeged index are identified.



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