Robert Jajcay: r-regular families of permutations and vertex-transitive graphs
Pozor! Čas predavanja (16.15) in predavalnica (J21, 3.06) sta spremenjena!
Povzetek. An r-regular family F of permutations on a set V contains for each pair of vertices u,v in V exactly r permutations f in F mapping u to v, f(u)=v. Previously, 1-regular families of graph automorphisms were used by Gauyacq to characterize the quasi-Cayley graphs; a class of vertex-transitive graphs that properly contains the class of Cayley graphs, shares many characteristics of the Cayley graphs, and is properly contained in the class of vertex-transitive graphs.
We introduce the concept of r-regular families to cover all vertex-transitive graphs, and to serve as a measurement of how far a vertex-transitive graph is from being Cayley.