TITLE:
On the Cozero-Divisor Graphs of Commutative Rings
AUTHORS:
Mojgan Afkham, Kazem Khashyarmanesh
KEYWORDS:
Clique Number; Connectivity; Cozero-Divisor Graph; Diameter; Direct Product; Girth; Rings of Polynomials; Rings of Power Series.
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.7,
July
5,
2013
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.