Gamma Graph Γ(Z_n)(γ) Of Zero Divisor Graph Of A Finite Commutative Ring Z_n

Abstract

Consider the family of γ-sets of a zero-divisor graph of finite commutative ring and define the γgraphs (γ) = ( of to be the graph whose vertice V(γ) corresponds 1-to-1 with the γ-sets , say S1 and S2, form an edge in E(γ) if there exist a vertex vÎ such that (i)v is adjacent to and (ii) and Using this definition, we investigate the interplay between the graph theoretic properties of and and the ring theoretic properties of Further, we prove that are an Eulerian and Hamiltonian.