A study on resistance matrix of graphs

2018/03/24 by Sarma, Deepak
#05B20 #05C12 #05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.09144

Abstract

In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance matrix in case of weighted graphs where all edge weights are positive definite matrices of given order.

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• Two Laplacians for the resistance distance matrix of a graph
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• On resistance matrices of weighted balanced digraphs
• The resistance distance of a dual number weighted graph