University of Primorska Faculty of Mathematics, Natural Sciences and Information Technologies
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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.

Archive
Datum in ura / Date and time: 17.5.21
(10:00 -- 11:00)
Predavalnica / Location: Zoom
Predavatelj / Lecturer: Blas Fernández (UP IAM, Slovenia)
Naslov / Title: On 2-Y-homogeneous and almost 2-Y-homogeneos distance-biregular graphs
Vsebina / Abstract:

Let G denote a distance-biregular 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: 

  1. for all i (1 \leq i \leq D-2) 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 i-1 from z is independent of the choice of x,y and z. 

  2. for all i (1 \leq i \leq D-1) 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 i-1 from z is independent of the choice of x,y and z. 

Distance-biregular graphs with the previous combinatorial structures are called almost 2-Y-homogeneous and 2-Y-homogeneous, respectively. Several examples will also be presented. This is joint work with Safet Penjić. 

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Everyone is welcome and encouraged to attend.