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Clique Complex Homology: A Combinatorial Invariant for Chordal Graphs

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  • Allen D. Parks

Abstract

It is shown that a geometric realization of the clique complex of a connected chordal graph is homologically trivial and as a consequence of this it is always the case for any connected chordal graph G that ∑_(k=1)^à ‰(G)â–’(-1)^(k-1) η_k (G)=1, where η_k (G) is the number of cliques of order k in G and à ‰(G) is the clique number of G.

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  • Allen D. Parks, 2013. "Clique Complex Homology: A Combinatorial Invariant for Chordal Graphs," International Journal of Sciences, Office ijSciences, vol. 2(07), pages 96-100, July.
    • Handle: RePEc:adm:journl:v:2:y:2013:i:7:p:96-100
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    Cited by:

    1. Allen D. Parks, 2015. "Observations Concerning Chordal Graph Polynomials," International Journal of Sciences, Office ijSciences, vol. 4(01), pages 36-39, January.

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