Title: K-domination number of products of two directed cycles and two directed paths

Authors: Ramy Shaheen

Addresses: Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria

Abstract: Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A subset S of the vertex set V(D) is a k-dominating set (k ≥ 1) of D if for each vertex v not in S there exists k vertices {u_i, ..., u_k} ⊆ S such that (u_i, v) is an arc of D for i = 1, ..., k. The k-domination number of D, k(D), is the cardinality of the smallest k-dominating set of D. The k-domination number (k ≥ 2) of the Cartesian products of two directed cycles, two directed paths and Cartesian products of a directed path and a cycle are determined. Also, we give k-domination number (k ≥ 2) of the direct product of two directed cycles and two directed paths.

Keywords: directed graph; directed cycle; directed paths; Cartesian product; direct product; k-domination number.

DOI: 10.1504/IJCSM.2018.091734

International Journal of Computing Science and Mathematics, 2018 Vol.9 No.2, pp.197 - 206

Received: 01 May 2016
Accepted: 12 Jun 2017
Published online: 14 May 2018 *

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