Displaying similar documents to “A Gallai-type equality for the total domination number of a graph”

The bondage number of graphs: good and bad vertices

Vladimir Samodivkin (2008)

Discussiones Mathematicae Graph Theory

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The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D. Any dominating set D of a graph G with |D| = γ(G) is called a γ-set of G. A vertex x of a graph G is called: (i) γ-good if x belongs to some γ-set and (ii) γ-bad if x belongs to no γ-set. The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph...

Domination Parameters of a Graph and its Complement

Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning (2018)

Discussiones Mathematicae Graph Theory

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A dominating set in a graph G is a set S of vertices such that every vertex in V (G) S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G. Placing constraints on a dominating set yields different domination parameters, including total, connected, restrained, and clique domination numbers. In this paper, we study relationships among domination parameters of a graph and its complement.

Chordal Graphs

Broderick Arneson, Piotr Rudnicki (2006)

Formalized Mathematics

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We are formalizing [9, pp. 81-84] where chordal graphs are defined and their basic characterization is given. This formalization is a part of the M.Sc. work of the first author under supervision of the second author.

Partitioning a graph into a dominating set, a total dominating set, and something else

Michael A. Henning, Christian Löwenstein, Dieter Rautenbach (2010)

Discussiones Mathematicae Graph Theory

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A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, Ars Comb. 89 (2008), 159-162) implies that every connected graph of minimum degree at least three has a dominating set D and a total dominating set T which are disjoint. We show that the Petersen graph is the only such graph for which D∪T necessarily contains all vertices of the graph.

The Distance Roman Domination Numbers of Graphs

Hamideh Aram, Sepideh Norouzian, Seyed Mahmoud Sheikholeslami (2013)

Discussiones Mathematicae Graph Theory

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Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value w(f) =∑v∈V f(v). The k-distance Roman domination number of a graph G, denoted by γkR (D), equals the minimum weight of a k-distance Roman dominating...