ON WEAK DOMINATION IN A ZERO DIVISOR GRAPH

Abstract

Let R be a commutative ring and let Γ(Zn) be the zero divisor graph of R. The zero-divisor graph of a ring is the graph(simple) whose vertex set is the set of non-zero zero-divisors, and an edge is drawn between two distinct vertices if their product is zero. For a graph Γ(Zn), a set $S⊆V(Γ(Zn)) is a weak dominating set if every vertex v in V(Γ(Zn))-S has a neighbour u in S such that the degree of u is not greater than the degree of v. The minimum cardinality of a weak dominating set of Γ(Zn) is the weak domination number, γw(Γ(Zn)).