Abstract
The b-vector (b1,b2…,bd) of a graph G is defined in terms of its clique vector (c1,c2…,cd) by the equation ∑i=1dbi(x+1)i−1= ∑i=1dcixi−1, where d is the largest cardinality of a clique in G. We study the relation of the b-vector of a chordal graph G with some structural properties of G. In particular, we show that the b-vector encodes different aspects of the connectivity and clique dominance of G. Furthermore, we relate the b-vector with the Betti numbers of the Stanley–Reisner ring associated to clique simplicial complex of G.
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