István Estélyi: Haar graphs over abelian groups and in general

Povzetek. Haar graphs or bi-Cayley graphs can be defined similarly to the well known Cayley graphs. One possible definition is the following. Let G be a given group and S its subset. The bipartite graphs H(G,S) have bipartition sets isomorphic to G and vertices g,h are connected iff h=gs for some s in S. They have been studied from different perspectives by M. Hladnik, D. Marušič, T. Pisanski and many others. Some of the questions in the area are finding the girth, eigenvalues, conditions of hamiltonicity and several other properties in terms of the group G and the generating set S. 

 

The talk is intended to serve as a brief outline of the problematics above.