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 ⊆ Zn, the set of all positive zero-divisors of the ring Zn such that V = S and (x, y) ∈ E if and only if y − x ≡ w(mod n) for some w ∈ V. If S = Zn, 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.
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