Total domination in graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1980 English Publisher:WileyJournal:Networks, volume 10, pages 211-219 (issn: 0028-3045, eissn: 1097-0037,

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Authors: Ernest J. Cockayne; R. M. Dawes; Stephen T. Hedetniemi;

doi: 10.1002/net.3230100304

Total domination in graphs

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Abstract

AbstractA set D of vertices of a finite, undirected graph G = (V, E) is a total dominating set if every vertex of V is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number of G (the largest order of a partition of G into total dominating sets).

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Keywords

Graph theory, total domination number, total domatic number, smallest total dominating set

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