Note on degree Kirchhoff index of graphs

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.

Keywords:

resistance distance (in graphs) , Kirchhoff index , degree Kirchhoff index , spectrum of graph , Laplacian spectrum of graph