Resistance Distance and Kirchhoff Index in Subdivision-Vertex and Subdivision-Edge Neighbourhood Coronae

Liu, Qun; Wang, Weizhong

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Ars Combinatoria

Volume 130
Pages: 29-41

Research article

Resistance Distance and Kirchhoff Index in Subdivision-Vertex and Subdivision-Edge Neighbourhood Coronae

^¹,², ^³

¹School of Mathematics and Statistics, Heri University, Gansu, Zhangye, 734000, P.R. China

²Department of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, P.R. China

³Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, PR China

Published: 31/01/2017

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Abstract

In this paper, formulas of the resistance distance for the arbitrary two-vertex resistance of $G$ , $H = G_{1} ⊡ G_{2}$ and $G_{1} ⊟ G_{2}$ in the electrical networks are obtained in a much simpler way. Furthermore, $K_{f} (G_{1} ⊡ G_{2})$ and $K_{f} (G_{1} ⊟ G_{2})$ can be expressed as a combination of $K_{f} (G_{1})$ and $K_{f} (G_{2})$ .

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Ars Combinatoria

Resistance Distance and Kirchhoff Index in Subdivision-Vertex and Subdivision-Edge Neighbourhood Coronae

Abstract

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