Quasi-Groups and r-Regular Families of Permutations in Algebraic Graph Theory

Resumen:

Cayley graphs - one of the central classes of  vertex-transitive graphs - are characterized by the existence of a group of automorphisms acting regularly on their vertex sets. The topic of the lecture will be a generalization of the concept of Cayley graphs to quasi-Cayley graphs characterized by the existence of a family of automorphisms acting regularly on the vertices. We will present the background and motivation behind this generalization, introduce some of their fundamental properties, discuss r-regular families of permutations, and explain their relevance within the class of vertex-transitive graphs.

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