Zero divisor graph associated to Γ−semigroup of Zn

Abstract

In this paper we have studied the zero divisor graph G₁(Z_n(Γ)) associated with a Γ−semigroup. Here we have taken two non empty sets Z_n and set Γ of non zero zero divisors of Z_n then Z_n(Γ) is a Γ−semi group. In this paper we have taken all the elements of Z_n as the vertices of the graph G₁(Z_n(Γ)) and two distinct vertices a and b are adjacent if and only if for any α∈Γ we have aαb=0. In this paper we have studied the degree of vertices of G₁(Z_n(Γ)), number of edges, girth, diameter, planarity, and traversibility of G₁(Z_n(Γ)).