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On the Cozero-Divisor Graphs of Commutative Rings
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
- 1 Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
- 2 Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
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Abstract
Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R , denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R , and two distinct vertices a and b in are adjacent if and only if and . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs and such as connectivity, diameter, girth, clique numbers and planarity. We also study the cozero-divisor graphs of the direct products of two arbitrary commutative rings.
KeywordsClique NumberConnectivityCozero-Divisor GraphDiameterDirect ProductGirthRings of PolynomialsRings of Power Series.
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