(SI) V predlaganem projektu bomo raziskovali tako imenovane razdaljno-regularne grafe. Ogrodja petih platonskih teles so primeri takšnih grafov. Izkaže se, da je teorija razdaljno-regularnih grafov povezana tudi z mnogimi drugimi področji matematike, kot so na primer teorija kodiranja, teorija reprezentacij in teorija ortogonalnih polinomov. Prrojekt je sestavljen iz dveh glavnih delov: študija Terwilliger-jevih algeber razdaljno regularnih grafov (preko nerazcepnih modulov), ter študija delovanj grup avtomorfizmov razdaljno-regularnih grafov.
(EN) Our research concerns a combinatorial object known as a graph. A graph is a finite set of vertices, together with a set of undirected arcs or edges, each of which connects a pair of distinct vertices. We say that vertices x; y are adjacent whenever x; y are connected by an edge. The concept of a graph is useful because mathematical as well as intuitive notions can be formulated in terms of adjacency. In our research we study graphs which are called distance-regular. The 1-skeletons of the five platonic solids provide examples of distanceregular graphs. The theory of distance-regular graphs is connected to some other areas of mathematics, such as coding theory, representation theory, and the theory of orthogonal polynomials.