The -vector of a graph is defined in terms of its clique vector by the equation where is the largest cardinality of a clique in . We study the relation of the -vector of a chordal graph with some structural properties of . In particular, we show that the -vector encodes different aspects of the connectivity and clique dominance of . Furthermore, we relate the -vector with the Betti numbers of the Stanley–Reisner ring associated to clique simplicial complex of .
"$b$-vectors of chordal graphs." J. Commut. Algebra 12 (4) 539 - 557, Winter 2020. https://doi.org/10.1216/jca.2020.12.539