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A study on the resistance matrix of a graph

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Abstract

In this article, we consider the resistance matrix of a connected graph. A connected graph is said to be resistance regular if all the row(column) sums of its resistance matrix are equal. We establish some necessary and sufficient conditions for a simple connected graph to be a resistance regular graph. Also, we find some relationship between the Laplacian matrix and the resistance matrix in the case of weighted graphs where all edge weights are positive definite matrices of given order.

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Authors and Affiliations

  1. Department of Agril. Statistics, Assam Agricultural University, Jorhat, 785013, India

    Deepak Sarma

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  1. Deepak Sarma
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Correspondence to Deepak Sarma.

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Communicated by S Sivaramakrishnan.

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Sarma, D. A study on the resistance matrix of a graph. Indian J Pure Appl Math 54, 299–311 (2023). https://doi.org/10.1007/s13226-022-00254-5

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  • DOI: https://doi.org/10.1007/s13226-022-00254-5

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