On the resistance regular graphs

Abstract

For a connected graph G, its resistance distance matrix is denoted by R(G). A graph is called resistance regular if all the row (or column) sums of R(G) are equal. We provide a necessary and sufficient condition for a simple connected graph to be resistance regular. Additionally, we establish sharp bounds for the resistance spectral radius and present various bounds for the resistance energy of G. Furthermore, we compute the resistance spectrum and resistance energy of some resistance regular graphs.