Mathematical Research Seminar
Mathematical research seminar is organized by the departments of Mathematics of two members of the University  UP FAMNIT and Andrej Marušič Institute (UP IAM), every Monday from October to June.
You are cordially invited to attend the lectures.
Let G denote a distancebiregular graph with bipartite parts Y and Y’. Let D denote the eccentricity of vertices in Y. Given a vertex z, let \Gamma_i(z) denote the set of all vertices which are at distance i from z. For vertices x and y, let \Gamma_{i,j}(x,y) denote the collection of all vertices which are at distance i from x and at distance j from y.
In this talk, we will show necessary and sufficient conditions on the intersection array of G for which the given graph has one of the following two combinatorial structures:

for all i (1 \leq i \leq D2) and for all x\in Y, y\in \G_2(x) and z \in \G_{i,i}(x,y) the number of vertices in \G_{1,1}(x,y) which are at distance i1 from z is independent of the choice of x,y and z.

for all i (1 \leq i \leq D1) and for all x\in Y, y\in \G_2(x) and z \in \G_{i,i}(x,y) the number of vertices in \G_{1,1}(x,y) which are at distance i1 from z is independent of the choice of x,y and z.
Distancebiregular graphs with the previous combinatorial structures are called almost 2Yhomogeneous and 2Yhomogeneous, respectively. Several examples will also be presented. This is joint work with Safet Penjić.