Codes in distance-regular graphs

Povzetek: First, I will introduce the concepts of distance-regular graphs and codes in graphs. Using triple intersection numbers, some feasible families of distance-regular graphs with codes will be found. For some of these families nonexistence can be shown, while for others, I will present some information about the structure, which might possibly lead to new constructions.

I will also present a new proof of uniqueness for both the Coxeter graph and the Sylvester graph, which is purely combinatorial and does not rely on results about larger graphs. Finally, I will present some results regarding the missing Moore graph and its subgraph on vertices at distance 2 from an edge.

Joint work with Aleksandar Jurišić.