Clique Complex Homology: A Combinatorial Invariant for Chordal Graphs

Allen D. Parks

International Journal of Sciences, 2013, vol. 2, issue 07, 96-100

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.

Keywords: algebraic graph theory; chordal graph; clique complex; hypergraph; homology; Mayer-Vietoris theorem; graph invariant; Euler-Poincaré formula (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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