On the resistance regular graphs

For a connected graph G, its resistance matrix is denoted by $R(G)$. If all the row(column) sums of $R(G)$ are equal, then G is said to be resistance regular. In $[13]$, J. Zhou et al. posed the question regarding the existence of a non-regular resistance regular graph. In this article, we establish that all resistance regular graphs are regular, thus conclusively answering Zhou's question by showing that no non-regular resistance regular graph exists. Also, we compute the resistance energies of some resistance regular graphs. Furthermore, we determine various bounds for the resistance energy and resistance spectral radius of $G.$