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Title: Efficient edge domination in regular graphs
Author: Cardoso, Domingos M.
Orestes Cerdeira, J.
Delorme, C.
Silva, P. C.
Keywords: Domination in graphs
Induced matchings
Regular graphs
Spectra of graphs
Edge dominating set
Graph theory
Issue Date: 2008
Publisher: Elsevier
Abstract: An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p ≥ 3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete. © 2008 Elsevier B.V. All rights reserved.
Peer review: yes
ISSN: 0166-218X
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Appears in Collections:DMat - Artigos

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