On the Cozero-Divisor Graphs of Commutative Rings

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.

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M. Afkham and K. Khashyarmanesh, "On the Cozero-Divisor Graphs of Commutative Rings," Applied Mathematics, Vol. 4 No. 7, 2013, pp. 979-985. doi: 10.4236/am.2013.47135.

Conflicts of Interest

The authors declare no conflicts of interest.

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