Efficient edge domination in regular graphs

13 An induced matching of a graph G is a matching having no two edges joined by14 an edge. An efficient edge dominating set of G is an induced matching M such that15 every other edge of G is adjacent to some edge in M. We relate maximum induced16 matchings and efficient edge dominating sets, showing that efficient edge dominating17 sets are maximum induced matchings, and that maximum induced matchings on18 regular graphs with efficient edge dominating sets are efficient edge dominating sets.19 A necessary condition for the existence of efficient edge dominating sets in terms20 of spectra of graphs is established. We also prove that, for arbitrary fixed p 3,21 deciding on the existence of efficient edge dominating sets on p-regular graphs is22 NP-complete.23 Key words: induced matchings, domination in graphs, regular graphs, spectra of24 graphs, NP-completeness.25 1991 MSC: 05C69, 05C7026 Preprint submitted to Elsevier Science 16th May 2006 

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Domingos Moreira Cardoso, J. Orestes Cerdeira, Charles Delorme, Pedro C. Silva
• Keywords: DAM 2008, Edge Dominating Sets, Efficient Edge, Maximum Induced Matchings