location:  Publications → journals → CMB
Abstract view

# 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
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 05C12 - Distance in graphs 05C35 - Extremal problems [See also 90C35]

 top of page | contact us | privacy | site map |