On Generalized Non-commuting Graph of a Finite Ring
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Let S and K be two subrings of a finite ring R. Then the generalized non-commuting graph of subrings S, K of R, denoted by ГS,K, is a simple graph whose vertex set is [Formula: see text], and where two distinct vertices a, b are adjacent if and only if [Formula: see text] or [Formula: see text] and [Formula: see text]. We determine the diameter, girth and some dominating sets for ГS,K. Some connections between ГS,K and Pr(S, K) are also obtained. Further, ℤ-isoclinism between two pairs of finite rings is defined, and we show that the generalized non-commuting graphs of two ℤ-isoclinic pairs are isomorphic under some conditions.
2011 ◽
Vol 10
(03)
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pp. 521-527
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2019 ◽
Vol 12
(05)
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pp. 1950081
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2021 ◽
Vol 2021
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pp. 1-9
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