• ON AN UNDIRECTED GRAPH STRUCTURE OF A COMMUTATIVE RING
Abstract
Let R be a commutative ring with unity and Z(R) be the set of all zero-divisors of R. For , the annihilator of is the set . The new annihilator graph of R, denoted by ANNG(R), is the undirected graph whose set of vertices is Z(R)* = Z(R) - {0}, and two distinct vertices and are adjacent if and only if . In this paper, we investigate the relationship among the new annihilator graph ANNG(R), the annihilator graph AG(R) and the zero-divisor graph G(R).
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