On the commuting graph of some non-commutative rings with unity
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چکیده مقاله:
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 $4K_2 cup K_6$.
منابع مشابه
on the commuting graph of some non-commutative rings with unity
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 ...
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عنوان ژورنال
دوره 05 شماره 04
صفحات 289- 294
تاریخ انتشار 2016-01-20
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