Efficient edge domination in regular graphs

被引：19

作者：

Cardoso, Domingos M. ^{[3
]}

Cerdeira, J. Orestes ^{[1
,2
]}

Delorme, Charles ^{[4
]}

Silva, Pedro C. ^{[1
,2
]}

机构：

[1] Univ Tecn Lisboa, Ctr Estudos Florestais, P-1349017 Lisbon, Portugal

[2] Univ Tecn Lisboa, Inst Super Agron, Dept Matemat, P-1349017 Lisbon, Portugal

[3] Univ Aveiro, Dept Matemat, P-3810193 Aveiro, Portugal

[4] Univ Paris 11, Rech Informat Lab, F-91405 Orsay, France

来源：

DISCRETE APPLIED MATHEMATICS | 2008年 / 156卷 / 15期

关键词：

Induced matchings; Domination in graphs; Regular graphs; Spectra of graphs; NP-completeness;

D O I：

10.1016/j.dam.2008.01.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：3060 / 3065

页数：6

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