The Maximum Number of Dominating Induced Matchings

A matching M of a graph G is a dominating induced matching (DIM) of G if every edge of G is either in M or adjacent with exactly one edge in M. We prove sharp upper bounds on the number μ(G) of DIMs of a graph G and characterize all extremal graphs. Our results imply that if G is a graph of order n,...

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Detalles Bibliográficos
Autores: Lin, Min Chih, Moyano, Verónica Andrea, Rautenbach, Dieter, Szwarcfiter, Jayme L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/42701
Acceso en línea:http://hdl.handle.net/11336/42701
Access Level:acceso abierto
Palabra clave:Dominating Induced Matching
Fibonacci Numbers
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:A matching M of a graph G is a dominating induced matching (DIM) of G if every edge of G is either in M or adjacent with exactly one edge in M. We prove sharp upper bounds on the number μ(G) of DIMs of a graph G and characterize all extremal graphs. Our results imply that if G is a graph of order n, then μ(G) ≤ 3n 3 ; μ(G) ≤ 4n 5 provided G is triangle-free; and μ(G) ≤ 4n−1 5 provided n ≥ 9 and G is connected.