A study on resistance matrix of graphs
Deepak Sarma
TL;DR
This paper investigates the properties of the resistance matrix in graphs, establishing conditions for resistance regularity in unweighted graphs and exploring relationships between Laplacian and resistance matrices in weighted graphs with positive definite edge weights.
Contribution
It provides new criteria for resistance regular graphs and links between Laplacian and resistance matrices in weighted graphs with positive definite weights.
Findings
Characterization of resistance regular graphs in unweighted cases
Relationships between Laplacian and resistance matrices for weighted graphs
Conditions involving positive definite edge weights
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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Taxonomy
TopicsGraph theory and applications · Graph Labeling and Dimension Problems · Advanced Graph Theory Research