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,...
| Autores: | , , , |
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| 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 |
| 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. |
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