Author
R. M. Dawes
Bio: R. M. Dawes is an academic researcher from University of Oregon. The author has contributed to research in topics: Vertex (geometry) & Independent set. The author has an hindex of 1, co-authored 1 publications receiving 532 citations.
Papers
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TL;DR: Results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number ofG (the largest order of a partition of G into total dominating sets) are obtained.
Abstract: A 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).
570 citations
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TL;DR: This paper offers a survey of selected recent results on total domination in graphs and defines a set S of vertices in a graph G if every vertex of G is adjacent to some vertex in S.
289 citations
TL;DR: In this paper, Nordhaus and Gaddum gave lower and upper bounds on the sum and product of the chromatic number of a graph and its complement, in terms of the order of the graph.
198 citations
TL;DR: It is shown that the problem of finding a minimum cardinality dominating set is NP-complete for split graphs and bipartite graphs.
178 citations
TL;DR: The following bibliography on Domination in Graphs has been compiled over the past six years at Clemson University, where it is expected that this bibliography will continue to grow at a steady rate.
157 citations