The structural properties of zero divisor difference digraphs

Abstract

A graph G = (V, E) is a proper zero-divisor difference graph if and only if there is a positive integer n and a set S ⊂ Z<inf>n</inf>, the set of all positive zero-divisors of the ring Z<inf>n</inf> such that V = S and (x, y) E if and only if y-x ≈ w(mod n) for some w V. If S = Z<inf>n</inf>, then the graph is called a zero-divisor difference graph. In this paper we discuss the characteristics and structural properties of zero-divisor difference graphs. i.e. We prove the results on connectedness, degree, planarity, isomorphism etc. of zero-divisor difference graphs depending on the value of n. © 2016 Author(s).