On regular sets in Cayley graphs

Xiaomeng Wang, Shou-Jun Xu, Sanming Zhou

Let $\Ga = (V, E)$ be a graph and $a,b$ nonnegative integers. An $(a,b)$-regular set in $\Ga$ is a nonempty proper subset $D$ of $V$ such that every vertex in $D$ has exactly $a$…