On clique convergent graphs
type: Item
instance of: scholarly article
title: On clique convergent graphs
zbMATH Open document ID: 0841.05094
DOI: 10.1007/BF01793007
author: Claudson F. Bornstein
author: Jayme L. Szwarcfiter
published in: Graphs and Combinatorics
publication date: 1996-07-14T00:00:00Z
review text: The clique graph \(K(G)\) of a graph \(G\) is defined as an intersection graph of the maximal cliques of \(G\). The authors investigate graphs for which an integer \(n\) exists such that \(K^n(G)\) is a trivial graph, where \(K^n(G)\) is the \(n\)th clique iterated graph of \(G\). The smallest integer \(n\) with the above property is called the index of \(G\). The cliques of \(G\) fulfill the Helly property if every family of pairwise intersecting cliques has nonempty intersection. The Helley defect is defined as the minimal integer \(n\) such that \(K^n(G)\) has the Helly property. The main result of the paper is that for arbitrary integers \(n\) there exists a graph \(G\) such that the Helly defect of \(G\) may exceed by \(n\) the difference of its index and diameter.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 811341
zbMATH Keywords: clique convergent graphs
zbMATH Keywords: clique graph
zbMATH Keywords: intersection graph
zbMATH Keywords: maximal cliques
zbMATH Keywords: clique iterated graph
zbMATH Keywords: index
zbMATH Keywords: Helly property
zbMATH Keywords: Helley defect
zbMATH Keywords: diameter
reviewed by: Ludovit Niepel
MaRDI profile type: Publication
cites work: Clique graphs and Helly graphs
cites work: Clique graphs of time graphs
cites work: Über iterierte Clique-Graphen
cites work: Convergence of iterated clique graphs
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description: scientific article; zbMATH DE number 811341