Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 18, Issue.: 3

Original Research Article

ON SIGNED DOMINATION NUMBER OF CARTESIAN PRODUCTS OF DIRECTED PATHS

 

ZHIQIANG ZHANG1 AND RAMY SHAHEEN2*

1School of Information Science and Engineering, Chengdu University, Chengdu, 610106, China.

2Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria.

Abstracts

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.