ON SIGNED DOMINATION NUMBER OF CARTESIAN PRODUCTS OF DIRECTED PATHS
ZHIQIANG ZHANG
School of Information Science and Engineering, Chengdu University, Chengdu, 610106, China.
RAMY SHAHEEN *
Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria.
*Author to whom correspondence should be addressed.
Abstract
Let D = (V, A) be a simple digraph of order n. Let f be a mapping of the vertex set V(D) into set {-1, 1}. If 
for each vertex v∈V(D), then f is called a signed dominating function on D. The signed domination number of a digraph D is γs(D) = min{ω(f ): f is a signed dominating function of D}. In this paper, we establish the exact values of the signed domination number of Cartesian product of two directed paths Pm and Pn for 2 ≤ m ≤ 7 and arbitrary n.
Keywords: Directed graph, directed path, Cartesian product, signed dominating function, signed domination number