On the Signed Domination Number of the Cartesian Product of Two Directed Cycles

Abstract

Let D be a finite simple directed graph with vertex set V ( D ) and arc set A ( D ). A function is called a signed dominating function (SDF) if for each vertex . The weight of f is defined by . The signed domination number of a digraph D is . Let C m × C n denotes the cartesian product of directed cycles of length m and n . In this paper, we determine the exact values of g s ( C m × C n ) for m = 8, 9, 10 and arbitrary n . Also, we give the exact value of g s ( C m × C n ) when m , (mod 3) and bounds for otherwise.