Luis Pedro Montejano, Luis Núñez-Betancourt. Source: Journal of Commutative Algebra, Volume 12, Number 4, 539--557.Abstract:
The [math] -vector [math] of a graph [math] is defined in terms of its clique vector [math] by the equation [math] where [math] is the largest cardinality of a clique in [math] . We study the relation of the [math] -vector of a chordal graph [math] with some structural properties of [math] . In particular, we show that the [math] -vector encodes different aspects of the connectivity and clique dominance of [math] . Furthermore, we relate the [math] -vector with the Betti numbers of the Stanley–Reisner ring associated to clique simplicial complex of [math] .