on the commuting graph of some non-commutative rings with unity
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abstract
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 :union: of complete graphs. finally, we prove that there are exactly five commuting graphs of non-commutative rings with unity up to twenty vertices and they are $3k_2,3k_4,7k_2, k_2 cup 2k_6$ and $4k_2 cup k_6$.
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Journal title:
journal of linear and topological algebra (jlta)جلد ۵، شماره ۰۴، صفحات ۲۸۹-۲۹۴
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