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Dominant-matching graphs

Igor' E. Zverovich, Olga I. Zverovich (2004)

Discussiones Mathematicae Graph Theory

We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.

Dominating and total dominating partitions in cubic graphs

Justin Southey, Michael Henning (2011)

Open Mathematics

In this paper, we continue the study of domination and total domination in cubic graphs. It is known [Henning M.A., Southey J., A note on graphs with disjoint dominating and total dominating sets, Ars Combin., 2008, 89, 159–162] that every cubic graph has a dominating set and a total dominating set which are disjoint. In this paper we show that every connected cubic graph on nvertices has a total dominating set whose complement contains a dominating set such that the cardinality of the total dominating...

Dominating bipartite subgraphs in graphs

Gábor Bacsó, Danuta Michalak, Zsolt Tuza (2005)

Discussiones Mathematicae Graph Theory

A graph G is hereditarily dominated by a class 𝓓 of connected graphs if each connected induced subgraph of G contains a dominating induced subgraph belonging to 𝓓. In this paper we characterize graphs hereditarily dominated by classes of complete bipartite graphs, stars, connected bipartite graphs, and complete k-partite graphs.

Dominating functions of graphs with two values

Bohdan Zelinka (1998)

Mathematica Bohemica

The Y -domination number of a graph for a given number set Y was introduced by D. W. Bange, A. E. Barkauskas, L. H. Host and P. J. Slater as a generalization of the domination number of a graph. It is defined using the concept of a Y -dominating function. In this paper the particular case where Y = { 0 , 1 / k } for a positive integer k is studied.

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