TITLE:
On Signed Domination of Grid Graph
AUTHORS:
Mohammad Hassan, Muhsin Al Hassan, Mazen Mostafa
KEYWORDS:
Grid Graph, Cartesian Product, Signed Dominating Function, Signed Domination Number
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.10 No.4,
October
27,
2020
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 γs(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 Pm and Pn for m = 6, 7 and arbitrary n.