The Signed Domination Number of Cartesian Product of Two Paths

Abstract

Let G be a finite connected simple graph with vertex set V ( G ) and edge set E ( G ). A function f : V ( G ) → {1,1} is a signed dominating function if for every vertex v ∈ V ( G ) , the closed neighborhood of v contains more vertices with function values 1 than with − 1. The signed domination number γ s ( G ) of G is the minimum weight of a signed dominating function on G . In this paper, we calculate The signed domination numbers of the Cartesian product of two paths P m and P n for m = 3, 4, 5 and arbitrary n .