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Type: Relatório
Title: Edge clique graphs and some classes of chordal graphs
Author(s)/Inventor(s): Cerioli, Márcia Rosana
Szwarcfiter, Jayme Luiz
Abstract: 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.
Keywords: Grafos cordal
Margens de grafos clique
Chordal graphs
Edge clique graphs
split graphs
Production unit: Instituto Tércio Pacitti de Aplicações e Pesquisas Computacionais
In: Relatório Técnico NCE
Issue: 2199
Issue Date: 31-Dec-1999
Publisher country: Brasil
Language: eng
Right access: Acesso Aberto
Citation: CERIOLI, M. R; SZWARCFITER, J. L. Edge clique graphs and some classes of chordal graphs. Rio de Janeiro: NCE, UFRJ, 1999. 17 p. (Relatório Técnico, 21/99)
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