let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...

Abstract A strong edge coloring of a graph G is proper such that every color class an induced matching. The minimum number colors required termed the chromatic index. In this paper we determine exact value index all unitary Cayley graphs. Our investigations reveal underlying product structure from which graphs emerge. We then go on to give tight bounds for Cartesian two trees, including formula...