On Signed Domination of Grid Graph

Abstract

Let G ( V , E ) be a finite connected simple graph with vertex set V ( G ). A function is a signed dominating function f : V ( G ) →{ − 1,1} if for every vertex v ∈ V ( G ), the sum of closed neighborhood weights of v is greater or equal to 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 = 6, 7 and arbitrary n .