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Degree Kirchhoff Index of Bicyclic Graphs

  Published:2016-10-11
 Printed: Mar 2017
  • Zikai Tang,
    College of Mathematics and Computer Science , Hunan Normal University, Changsha, Hunan 410081, P. R. China
  • Hanyuan Deng,
    College of Mathematics and Computer Science , Hunan Normal University, Changsha, Hunan 410081, P. R. China
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Abstract

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 degree Kirchhoff index, resistance distance, bicyclic graph, extremal graph
MSC Classifications: 05C12, 05C35 show english descriptions Distance in graphs
Extremal problems [See also 90C35]
05C12 - Distance in graphs
05C35 - Extremal problems [See also 90C35]
 

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