on quasi-zero divisor graphs of non-commutative rings

Let $r$ be an associative ring with identity. a ring $r$ is called reversible if $ab=0$, then $ba=0$ for $a,bin r$. the quasizerodivisor graph of $r$, denoted by $gamma^*(r)$ is an undirected graph with all nonzero zerodivisors of $r$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin r setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such that $xry=0$ or $yrx=0$. in this paper, we determine the diameter and girth of $gamma^*(r)$. we show that  the  zerodivisor graph of $r$ denoted by $gamma(r)$, is an induced subgraph of $gamma^*(r)$. also, we investigate when $gamma^*(r)$ is identical to $gamma(r)$. moreover, for a reversible ring $r$, we study the diameter and girth of $gamma^*(r[x])$ and we investigate when $gamma^*(r[x])$ is identical to $gamma(r[x])$.