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Characterization of rings with genus two cozero-divisor graphs

Praveen MathilBarkha BalodaJitender Kumar
Dec 2022
摘要
Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$ is anundirected simple graph whose vertices are the set of all non-zero and non-unitelements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and onlyif $x \notin Ry$ and $y \notin Rx$. The reduced cozero-divisor graph of a ring$R$, is an undirected simple graph whose vertex set is the set of allnontrivial principal ideals of $R$ and two distinct vertices $(a)$ and $(b)$are adjacent if and only if $(a) \not\subset (b)$ and $(b) \not\subset (a)$. Inthis paper, we characterize all classes of finite non-local commutative ringsfor which the cozero-divisor graph and reduced cozero-divisor graph is of genustwo.
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