Maximizing the number of spanning trees in KnKn-complements of asteroidal graphs

In this paper we introduce the class of graphs whose complements are asteroidal (star-like) graphs and derive closed formulas for the number of spanning trees of its members. The proposed results extend previous results for the classes of the multi-star and multi-complete/star graphs. Additionally, we prove maximization theorems that enable us to characterize the graphs whose complements are asteroidal graphs and possess a maximum number of spanning trees.