Defensive alliances in regular graphs and circulant graphs
In this paper we study defensive alliances in some regular graphs. We determine which subgraphs could a critical defensive alliance of a graph $G$ induce, if $G$ is $6$-regular and the cardinality of the alliance is at most $8$. In particular, we study the case of circulant graphs, i.e. Cayley graph...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/2284 |
| Acceso en línea: | https://hdl.handle.net/2117/2284 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory alliance induced subgraph Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory |
| Sumario: | In this paper we study defensive alliances in some regular graphs. We determine which subgraphs could a critical defensive alliance of a graph $G$ induce, if $G$ is $6$-regular and the cardinality of the alliance is at most $8$. In particular, we study the case of circulant graphs, i.e. Cayley graphs on a cyclic group. The critical defensive alliances of a circulant graph of degree at most $6$ are completely determined. For the general case, we give tight lower and upper bounds on the alliance number of a circulant graph with $d$ generators. |
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