The Zero Divisor Graph of the Ring Z_(2^2 p)

Abstract

In this paper, we consider the crossing number and the chromatic number of the zero divisor graph Γ(Z_(2^2 p)) to show that this type of zero divisor graphs is bipartite graph, and the smallest cycle in Γ(Z_(2^2 p)) is of length four this implies that the girth is equal four.

Keywords

• bipartite graph, crossing number, girth, planar graph, zero divisor graph of the ring z_(2^2 p).