Resistance Distance and Kirchhoff Index of the Corona-Vertex and the Corona-Edge of Subdivision Graph

Abstract

The resistance distance is widely used in random walk, electronic engineering, and complex networks. One of the main topics in the study of the resistance distance is the computation problem. The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge of G. Two classes of new corona graphs, the corona-vertex of the subdivision graph G1*G2 and the corona-edge of the subdivision graph G1 * G2, were defined by Lu and Miao. The adjacency spectrum and the signless Laplacian spectrum of the two new graph operations were computed when G1 is an arbitrary graph and G2 is an r2-regular graph. In this paper, we give the closed-form formulas for the resistance distance and Kirchhoff index of G1*G2 and G1 * G2 in terms of the resistance distance and Kirchhoff index of the factor graphs.

Keywords

• Kirchhoff index
• resistance distance
• group inverse