Abstract
This chapter presents several new constructions and examples of highly symmetric perfect regraphs. They are based on a simple observation that perfect regraphs are closely related to morphisms of boolean lattices into partition lattices. This allows one to apply results about partition representations of arbitrary lattices to construct new perfect regraphs. The chapter presents examples of perfect regraphs with large automorphism groups. Mostly they come from boolean sublattices of the subgroup lattices of finite groups. Boolean sublattices of the subgroup lattices are not very hard to find. The chapter also describes the general construction of perfect regraphs with a permutation extension property.
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