A note on total graph of ℤ n

Abstract

Let R be a commutative ring and Z(R) be its set of zero-divisors. The total graph of R, denoted by T Γ (R), is the (undirected) graph with vertices R, and for distinct x, y ∈ R, the vertices x and y are adjacent if and only if x + y ∈ Z(R). In this paper we obtain certain fundamental properties of the total graph on ℤ n . Also we find independent number and clique number of T Γ (ℤ n ).