Contractibility and the clique graph operator

To any graph G we can associate a simplicial complex Δ ( G ) whose simplices are the complete subgraphs of G , and thus we say that G is contractible whenever Δ ( G ) is so. We study the relationship between contractibility and K -nullity of G , where G is called K - null if some iterated clique gra...

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Bibliographic Details
Published in:Discrete mathematics 2008-08, Vol.308 (16), p.3461-3469
Main Authors: LARRION, F, PIZANA, M. A, VILLARROEL-FLORES, R
Format: Article
Language:English
Subjects:
Algebraic topology
Applied sciences
Clique graphs
Computer science
control theory
systems
Contractibility
Exact sciences and technology
Homotopy type
Information retrieval. Graph
Mathematics
Sciences and techniques of general use
Theoretical computing
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:To any graph G we can associate a simplicial complex Δ ( G ) whose simplices are the complete subgraphs of G , and thus we say that G is contractible whenever Δ ( G ) is so. We study the relationship between contractibility and K -nullity of G , where G is called K - null if some iterated clique graph of G is trivial. We show that there are contractible graphs which are not K -null, and that any graph whose clique graph is a cone is contractible.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2007.07.004