On the domination number of the cartesian product of the cycle of length n and any graph

El-Zahar M. ; Khamis, Soheir ; Nazzal K. 


Abstract


Let γ (G) denote the domination number of a graph G and let C n □ G denote the cartesian product of C n , the cycle of length n ≥ 3, and G. In this paper, we are mainly concerned with the question: which connected nontrivial graphs satisfy γ (C n □ G) = γ (C n ) γ (G)? We prove that this equality can only hold if n ≡ 1 (mod 3). In addition, we characterize graphs which satisfy this equality when n = 4 and provide infinite classes of graphs for general n ≡ 1 (mod 3). © 2006 Elsevier B.V. All rights reserved.


Other data

Issue Date 15-Feb-2007
Journal Discrete Applied Mathematics 
URI http://research.asu.edu.eg/123456789/1123
DOI 4
515
https://api.elsevier.com/content/abstract/scopus_id/33845972252
155
10.1016/j.dam.2006.07.003


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