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Deng, Hanyuan; Tang, Zikai
Degree Kirchhoff index of bicyclic graphs
Let $G$ be a connected graph with vertex set $V(G)$. The degree Kirchhoff index of $G$ is defined as $S'(G) =\sum_{\{u,v\}\subseteq V(G)}d(u)d(v)R(u,v)$, where $d(u)$ is the degree of vertex $u$, and $R(u, v)$ denotes the resistance distance between vertices $u$ and $v$. In this paper, we characterize the graphs having maximum and minimum degree Kirchhoff index among all $n$-vertex bicyclic graphs with exactly two cycles.

Keywords:degree Kirchhoff index, resistance distance, bicyclic graph, extremal graph
Categories:05C12, 05C35

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