Dominating Cartesian products of cycles
نویسندگان
چکیده
منابع مشابه
Dominating Cartesian Products of Cycles
Let y(G) be the domination number of a graph G and let G U H denote the Cartesian product of graphs G and H. We prove that y(X) = (nr= ,nr)/(2m + l), where X = C1 0 CZ 0 ... 0 C, and all nt = ICkIr 1 < k < m, are multiples of 2m + 1. The methods we use to prove this result immediately lead to an algorithm for finding minimum dominating sets of the considered graphs. Furthermore the domination n...
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The study of domination in Cartesian products has received its main motivation from attempts to settle a conjecture made by V.G. Vizing in 1968. He conjectured that γ(G)γ(H) is a lower bound for the domination number of the Cartesian product of any two graphs G and H. Most of the progress on settling this conjecture has been limited to verifying the conjectured lower bound if one of the graphs ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1995
ISSN: 0166-218X
DOI: 10.1016/0166-218x(93)e0167-w