Note on degree Kirchhoff index of graphs

Document Type : Research Paper


1 University of Kashan

2 University of Kragujevac Kragujevac, Serbia


The degree Kirchhoff index of a connected graph $G$ is defined as‎ ‎the sum of the terms $d_i\,d_j\,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $G$‎. ‎Bounds for the degree Kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎The special case of regular graphs is analyzed‎.


Main Subjects

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Volume 2, Issue 3 - Serial Number 3
September 2013
Pages 43-52
  • Receive Date: 12 July 2013
  • Revise Date: 28 August 2013
  • Accept Date: 28 August 2013
  • Published Online: 01 September 2013