let $g$ be a finite group. an element $gin g$ is called non-vanishing, if for every irreducible complex character $chi$ of $g$, $chi(g)neq 0$. the bi-cayley graph $bcay(g,t)$ of $g$ with respect to a subset $tsubseteq g$, is an undirected graph with vertex set $gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin g, tin t}$. let $nv(g)$ be the set of all non-vanishing element...
