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Ars Combinatoria

  • Research article

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

Qun Liu1,2, Weizhong Wang3
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

Abstract

In this paper, formulas of the resistance distance for the arbitrary two-vertex resistance of \(G\), \(H = G_1 \boxdot G_2\) and \(G_1 \boxminus G_2\) in the electrical networks are obtained in a much simpler way. Furthermore, \(K_f(G_1 \boxdot G_2)\) and \(K_f(G_1 \boxminus G_2)\) can be expressed as a combination of \(K_f(G_1)\) and \(K_f(G_2)\).

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Citation
Qun Liu, Weizhong Wang. Resistance Distance and Kirchhoff Index in Subdivision-Vertex and Subdivision-Edge Neighbourhood Coronae[J], Ars Combinatoria, Volume 130. 29-41. .