Efficient edge domination problems in graphs
Information Processing Letters
Regular codes in regular graphs are difficult
Discrete Mathematics
Solving the weighted efficient edge domination problem on bipartite permutation graphs
Discrete Applied Mathematics
New results on induced matchings
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Perfect edge domination and efficient edge domination in graphs
Discrete Applied Mathematics
An Atlas of Graphs (Mathematics)
An Atlas of Graphs (Mathematics)
Graph Theory, Computational Intelligence and Thought
On the complexity of the dominating induced matching problem in hereditary classes of graphs
Discrete Applied Mathematics
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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.