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arXiv · 2212.12900

Characterization of rings with genus two cozero-divisor graphs

Praveen Mathil·Barkha Baloda·Jitender Kumar
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Abstract

Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$ is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $x \notin Ry$ 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 all nontrivial principal ideals of $R$ and two distinct vertices $(a)$ and $(b)$ are adjacent if and only if $(a) \not\subset (b)$ and $(b) \not\subset (a)$. In this paper, we characterize all classes of finite non-local commutative rings for which the cozero-divisor graph and reduced cozero-divisor graph is of genus two.

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Praveen Mathil, Barkha Baloda, Jitender Kumar. 2022-12-25. Characterization of rings with genus two cozero-divisor graphs. https://arxiv.org/abs/2212.12900

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