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arXiv · 1611.04219

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

Qun Liu·Jia-Bao Liu·Shaohui Wang·Masoud Karimi
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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 $\cite{PL}$, two classes of new corona graphs, the corona-vertex of the subdivision graph $G_{1}\diamondsuit G_{2}$ and corona-edge of the subdivision graph $G_{1}\star G_{2}$ were defined. The adjacency spectrum and the signless Laplacian spectrum of the two new graphs were computed when $G_{1}$ is an arbitrary graph and $G_{2}$ is an $r$-regular graph. In this paper, we give the formulate of the resistance distance and the Kirchhoff index in $G_{1}\diamondsuit G_{2}$ and $G_{1}\star G_{2}$ when $G_{1}$ and $G_{2}$ are arbitrary graphs. These results generalize them in $\cite{PL}$.

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Qun Liu, Jia-Bao Liu, Shaohui Wang, Masoud Karimi. 2016-11-14. Resistance distance and Kirchhoff index in the corona-vertex and the corona $-$ edge of subdivision graph. https://arxiv.org/abs/1611.04219

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