Resistance distance and Kirchhoff index in the corona-vertex and the corona - edge of subdivision graph

2016/11/14 by Liu, Qun, Liu, Jia-Bao, Wang, Shaohui +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.04219

Abstract

The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge of G. In \citePL, two classes of new corona graphs, the corona-vertex of the subdivision graph G₁\diamondsuit G₂ and corona-edge of the subdivision graph G₁⋆ G₂ were defined. The adjacency spectrum and the signless Laplacian spectrum of the two new graphs were computed when G₁ is an arbitrary graph and G₂ is an r-regular graph. In this paper, we give the formulate of the resistance distance and the Kirchhoff index in G₁\diamondsuit G₂ and G₁⋆ G₂ when G₁ and G₂ are arbitrary graphs. These results generalize them in \citePL.

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