On the Cozero-Divisor Graphs of Commutative Rings

• 作者: Kazem Khashyarmanesh Mojgan Afkham
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: CLIQUE Number Connectivity Cozero-Divisor Graph Diameter Direct Product GIRTH RINGS of POLYNOMIALS RINGS of Power Series.
• 年，卷（期）: 2013,（7）
• 页码范围: 979-985
• 页数: 7页
• 分类号: O1

摘要

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.