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Showing papers on "Dominating set published in 1980"


Journal ArticleDOI
01 Sep 1980-Networks
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


Journal ArticleDOI
TL;DR: In this article, it was shown that the edge dominating set problem for graphs is $NP$-complete even when restricted to planar or bipartite graphs of maximum degree 3.
Abstract: We prove that the edge dominating set problem for graphs is $NP$-complete even when restricted to planar or bipartite graphs of maximum degree 3. We show as a corollary that the minimum maximal matching and the achromatic number problems are $NP$-complete. A new linear time algorithm for finding minimum independent edge dominating sets in trees is described, based on an observed relationship between edge dominating sets and independent sets in total graphs.

415 citations