ON SIGNED DOMINATION NUMBER OF CARTESIAN PRODUCTS OF DIRECTED PATHS

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Published: 2017-06-05

Page: 113-119


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


How to Cite

ZHANG, Z., & SHAHEEN, R. (2017). ON SIGNED DOMINATION NUMBER OF CARTESIAN PRODUCTS OF DIRECTED PATHS. Asian Journal of Mathematics and Computer Research, 18(3), 113–119. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1044

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