Robert Jajcay: Generalized Edge-Regular Graphs

Povzetek. Edge-regular graphs are regular graphs in which each edge is contained in the same number of triangles. We generalize this uniformity property to graphs of higher girths than 3, and consider k-regular graphs of girth g in which each edge is contained in the same number of g-cycles. We present some introductory existence results together with a number of bounds and limitations that form a basis for a theory of generalized edge-regular graphs. We also consider the connections to vertex-, edge- and arc-transitive graphs.

The presented results come of joint work with Stefko Miklavic and Gyorgy Kiss.