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.