Guide Domination in graphs: advanced topics

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On the Injective Equitable Domination of Graphs

According to Goddard and Henning , it is not known if the bound for planar diameter-3 graphs is sharp, but MacGillivray and Seyffarth gave an example of such of graph with domination number 6. The total domination number and ordinary domination number satisfy. Precomputed dominating sets for many named graphs can be obtained in the Wolfram Language using GraphData [ graph , "DominationNumber" ].

The following table summarizes values of the domination number for various special classes of graphs. Portions of this entry contributed by Nicolas Bray. Alikhani, S.

Domination in Graphs: Advanced Topics

Clark, W. Combinatorics 7 , No. Garey, M. New York: W.

Graph Theory: 50. Maximum vs Maximal

Freeman, p. Goddard, W.

Henning, M. Graph Th.

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Haynes, T. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination. Bounds on the Domination Number. Domination Independence and Irredundance. Efficiency Redundancy and Their Duals. Changing and Unchanging Domination. Conditions on the Dominating Set.

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Varieties of Domination. Condition: New.

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