We determine the number of edges of the zero-divisor graph of the direct product of finitely many finite non-commutative rings or semigoups.

Many authors studied the graph theory in connection with commutative semigroups and commutative and noncommutative rings as we can refer to references. For example, Beck 1 associated to any commutative ring R its zero-divisor graph G R whose vertices are the zero-divisors of R including 0 , with two vertices a, b joined by an edge in case ab 0. Also, DeMeyer et al. 2 defined the zero-divisor gr...

In this article we introduce the zero-divisor graphs ?P(X) and ?P? (X) of two rings CP(X) CP? (X); here P is an ideal closed sets in X aggregate those functions C(X), whose support lie on P. analogue ring C?(X). We determine when weakly graph W?P(X) coincides with ?P(X). find out conditions topology X, under-which (respectively, (X)) becomes triangulated/ hypertriangulated. realize that a compl...

This work aims to introduce and study a new kind of divisor graph which is called idempotent graph, it denoted by . Two non-zero distinct vertices v1 v2 are adjacent if only , for some non-unit element We establish fundamental properties as well it’s connection with also planarity this graph.