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- W2611872436 abstract "Let $S$ be a subring of a finite ring $R$ and $C_R(S) = {r in R : rs = sr ;forall; s in S}$. The relative non-commuting graph of the subring $S$ in $R$, denoted by $Gamma_{S, R}$, is a simple undirected graph whose vertex set is $R setminus C_R(S)$ and two distinct vertices $a, b$ are adjacent if and only if $a$ or $b in S$ and $ab neq ba$. In this paper, we discuss some properties of $Gamma_{S, R}$, determine diameter, girth, some dominating sets and chromatic index for $Gamma_{S, R}$. Also, we derive some connections between $Gamma_{S, R}$ and the relative commuting probability of $S$ in $R$. Finally, we show that the relative non-commuting graphs of two relative $Z$-isoclinic pairs of rings are isomorphic under some conditions." @default.
- W2611872436 created "2017-05-12" @default.
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- W2611872436 date "2017-05-05" @default.
- W2611872436 modified "2023-09-27" @default.
- W2611872436 title "Relative non-commuting graph of a finite ring" @default.
- W2611872436 hasPublicationYear "2017" @default.
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