FUZZY ZERO DIVISOR GRAPH IN A COMMUTATIVE RING

FUZZY ZERO DIVISOR GRAPH IN A COMMUTATIVE RING

A. Kuppan, J. Ravi Sankar

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Abstract

Let R be a commutative ring and let Γ(Zn) be the zero divisor graph of a commutative ring R, whose vertices are non-zero zero divisors of Zn, and such that the two vertices u, v are adjacent if n divides uv. In this paper, we introduce the concept of fuzzy zero zivisor graph in a commutative ring and also discuss the some special cases of Γf (Z2p), Γf (Z3p), Γf (Z5p), Γf (Z7p) and Γf (Zpq). Throughout this paper we denote the Fuzzy Zero Divisor Graph(FZDG) by Γf (Zn ).

Keywords

Fuzzy graph, Zero divisor graph, Fuzzy zero divisor graph(FZDG).