On total domination in the Cartesian product of graphs
نویسندگان
چکیده
منابع مشابه
Integer domination of Cartesian product graphs
Given a graph G, a dominating set D is a set of vertices such that any vertex not in D has at least one neighbor in D. A {k}-dominating multiset Dk is a multiset of vertices such that any vertex in G has at least k vertices from its closed neighborhood in Dk when counted with multiplicity. In this paper, we utilize the approach developed by Clark and Suen (2000) to prove a ‘‘Vizing-like’’ inequ...
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Let γ {k} t (G) denote the total {k}-domination number of graph G, and let G H denote the Cartesian product of graphs G and H . In this paper, we show that for any graphs G and H without isolated vertices, γ {k} t (G)γ {k} t (H) ≤ k(k + 1)γ {k} t (G H). As a corollary of this result, we have γt (G)γt (H) ≤ 2γt (G H) for all graphs G and H without isolated vertices, which is given by Pak Tung Ho...
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Given a graph G, a dominating set D is a set of vertices such that any vertex in G has at least one neighbor (or possibly itself) in D. A {k}-dominating multiset Dk is a multiset of vertices such that any vertex in G has at least k vertices from its closed neighborhood in Dk when counted with multiplicity. In this paper, we utilize the approach developed by Clark and Suen (2000) and properties ...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2018
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2039