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- W2964282363 abstract "Let $R$ be a finite ring and $rin R$. The $r$-noncommuting graph of $R$, denoted by $Gamma_R^r$, is a simple undirected graph whose vertex set is $R$ and two vertices $x$ and $y$ are adjacent if and only if $[x,y] neq r$ and $-r$. In this paper, we study several properties of $Gamma_R^r$. We show that $Gamma_R^r$ is not a regular graph, a lollipop graph and complete bipartite graph. Further, we consider an induced subgraph of $Gamma_R^r$ (induced by the non-central elements of $R$) and obtained some characterizations of $R$." @default.
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- W2964282363 date "2019-07-24" @default.
- W2964282363 modified "2023-09-27" @default.
- W2964282363 title "On r-noncommuting graph of finite rings" @default.
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