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...

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Detalles Bibliográficos
Autores: Cerioli, Márcia Rosana, Szwarcfiter, Jayme Luiz
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
Descripción
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.