Minimal graphs with disjoint dominating and total dominating sets
نویسندگان
چکیده
منابع مشابه
On graphs with disjoint dominating and 2-dominating sets
A DD2-pair of a graph G is a pair (D,D2) of disjoint sets of vertices of G such that D is a dominating set and D2 is a 2-dominating set of G. Although there are infinitely many graphs that do not contain a DD2-pair, we show that every graph with minimum degree at least two has a DD2-pair. We provide a constructive characterization of trees that have a DD2-pair and show that K3,3 is the only con...
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A set S of vertices in a graph G is a total dominating set of G if every vertex is adjacent to a vertex in S. A fundamental problem in total domination theory in graphs is to determine which graphs have two disjoint total dominating sets. In this paper, we solve this problem and provide a constructive characterization of the graphs that have two disjoint total dominating sets.
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A set S of vertices in a graph G(V,E) is called a dominating set if every vertex v ∈ V is either an element of S or is adjacent to an element of S. A set S of vertices in a graph G(V,E) is called a total dominating set if every vertex v ∈ V is adjacent to an element of S. The domination number of a graph G denoted by γ(G) is the minimum cardinality of a dominating set in G. Respectively the tot...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2021
ISSN: ['1234-3099', '2083-5892']
DOI: https://doi.org/10.7151/dmgt.2433