Clique Complex Homology: A Combinatorial Invariant for Chordal Graphs
Allen Parks · RePEc: Research Papers in Economics · 2013
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) Îá_k (G)=1, where Îá_k (G) is the number of cliques of order k in G and à ‰(G) is the clique number of G.