Edge clique graphs and some classes of chordal graphs
The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. This class of graphs has been introduced by Albertson and Collins (1984). Although many interesting properties of it have been since stu...
| Autores: | , |
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| Tipo de recurso: | informe técnico |
| Estado: | Versión publicada |
| Fecha de publicación: | 1999 |
| País: | Brasil |
| Institución: | Universidade Federal do Rio de Janeiro (UFRJ) |
| Repositorio: | Repositório Institucional da UFRJ |
| Idioma: | inglés |
| OAI Identifier: | oai:pantheon.ufrj.br:11422/2658 |
| Acceso en línea: | http://hdl.handle.net/11422/2658 |
| Access Level: | acceso abierto |
| Palabra clave: | Grafos cordal Margens de grafos clique Chordal graphs Edge clique graphs split graphs CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO |
| Sumario: | The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. This class of graphs has been introduced by Albertson and Collins (1984). Although many interesting properties of it have been since studied, we do not know complete characterizations of edge clique graphs of any non trivial class of graphs. In this paper, we describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlikethreshold, split and threshold graphs. In special, a known necessary condition for a graph to be an edge clique graph is that the sizes of all maximal cliques and intersections of ma.ximal cliques ought to be triangular numbers. We show that this condition is also suflicient for starlike-threshold graphs. |
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