let r be a non-commutative ring with unity. the commuting graph of $r$ denoted by $gamma(r)$, is a graph with a vertex set $rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if $ab=ba$. in this paper, we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$. it is shown that, $gamma(r)$ is the disjoint ...
