  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 $G.$
