Author(s)

Mohammad Hassan, Muhsin Al Hassan, Mazen Mostafa

Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria.

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.

Path, Cartesian Product, Signed Dominating Function, Signed Domination Number

Hassan, M. , Al Hassan, M. and Mostafa, M. (2020) The Signed Domination Number of Cartesian Product of Two Paths. Open Journal of Discrete Mathematics, 10, 45-55. doi: 10.4236/ojdm.2020.102005.