Resistance Distance in H -Join of Graphs G 1, G 2, …, G k

Li Zhang, Jing Zhao, Jia-Bao Liu and Micheal Arockiaraj
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Li Zhang: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Jing Zhao: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Jia-Bao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Micheal Arockiaraj: Department of Mathematics, Loyola College, Chennai 600034, India

Mathematics, 2018, vol. 6, issue 12, 1-10

Abstract: In view of the wide application of resistance distance, the computation of resistance distance in various graphs becomes one of the main topics. In this paper, we aim to compute resistance distance in H -join of graphs G 1 , G 2 , … , G k . Recall that H is an arbitrary graph with V ( H ) = { 1 , 2 , … , k } , and G 1 , G 2 , … , G k are disjoint graphs. Then, the H -join of graphs G 1 , G 2 , … , G k , denoted by ? H { G 1 , G 2 , … , G k } , is a graph formed by taking G 1 , G 2 , … , G k and joining every vertex of G i to every vertex of G j whenever i is adjacent to j in H . Here, we first give the Laplacian matrix of ? H { G 1 , G 2 , … , G k } , and then give a { 1 } -inverse L ( ? H { G 1 , G 2 , … , G k } ) { 1 } or group inverse L ( ? H { G 1 , G 2 , … , G k } ) # of L ( ? H { G 1 , G 2 , … , G k } ) . It is well know that, there exists a relationship between resistance distance and entries of { 1 } -inverse or group inverse. Therefore, we can easily obtain resistance distance in ? H { G 1 , G 2 , … , G k } . In addition, some applications are presented in this paper.

Keywords: graph; Laplacian matrix; resistance distance; group inverse (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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