A study on the resistance matrix of a graph

Deepak Sarma ()
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Deepak Sarma: Assam Agricultural University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 299-311

Abstract: 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.

Keywords: Connected graph; Laplacian matrix; Resistance distance; Moore Penrose inverse; (1)-inverse; 05C50; 05C12; 05B20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00254-5

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