  Simplicial complexes are a popular tool used to model higher-order
interactions between elements of complex social and biological systems. In this
paper, we study some combinatorial aspects of a class of simplicial complexes
created by a graph product, which is an extension of the pseudo-fractal
scale-free web. We determine explicitly the independence number, the domination
number, and the chromatic number. Moreover, we derive closed-form expressions
for the number of acyclic orientations, the number of root-connected acyclic
orientations, the number of spanning trees, as well as the number of perfect
matchings for some particular cases.
