On a Vizing-like conjecture for direct product graphs

Sandi Klavẑar, Blaẑ Zmazek
1996 Discrete Mathematics  
Let 7(G) be the domination number of a graph G, and let G ×H be the direct product of graphs G and H. It is shown that for any k t> 0 there exists a graph G such that 7(G × G) ~< 7(G) 2 -k. This in particular disproves a conjecture from [5] .
doi:10.1016/0012-365x(96)00032-5 fatcat:btwrhsi7kfdp7hggsv5hzud7v4