Signed Domination Number of the Directed Cylinder

Abstract

In a digraph D = ( V ( D ) , A ( D ) ) , a two-valued function f : V ( D ) → { - 1 , 1 } defined on the vertices of D is called a signed dominating function if f ( N - [ v ] ) ≥ 1 for every v in D. The weight of a signed dominating function is f ( V ( D ) ) = ∑ v ∈ V ( D ) f ( v ) . The signed domination number γ s ( D ) is the minimum weight among all signed dominating functions of D. Let P m × C n be the Cartesian product of directed path P m and directed cycle C n . In this paper, the exact value of γ s ( P m × C n ) is determined for any positive integers m and n.