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: 1.3.21
(10:00 -- 11:00)
Predavalnica / Location: Zoom
Predavatelj / Lecturer: Safet Penjić (UP FAMNIT and UP IAM, Slovenia)
Naslov / Title: On a certain families of a symmetric association schemes with d+1 classes
Vsebina / Abstract:

Let Γ denote an undirected, connected, regular graph with vertex set X, adjacency matrix A, and d+1 distinct eigenvalues. Let {\cal A}={\cal A}(Γ) denote the subalgebra of Mat_X(C) generated by A. We refer to {\cal A} as the {\em adjacency algebra} of Γ. In this talk, we investigate the algebraic and combinatorial structure of Γ for which the adjacency algebra {\cal A} is closed under Hadamard multiplication. In particular, under this simple assumption, we show the following: (i) {\cal A} has a standard basis {I,F_1,…,F_d}; (ii) for every vertex there exists identical distance-faithful intersection diagram of Γ with d+1 cells; (iii) the graph Γ is quotient-polynomial; and (iv) if we pick F∈{I,F_1,…,F_d} then F has d+1 distinct eigenvalues if and only if span{I,F_1,…,F_d}=span{I,F,…,F^d}. We describe the combinatorial structure of quotient-polynomial graphs with diameter 2 and 4 distinct eigenvalues.

This is joint work with Miquel À. Fiol.

This talk is based on one part of the preprint available at https://arxiv.org/abs/2009.05343

We are looking forward to meeting at the video-conference. Join Zoom Meeting HERE!


Everyone is welcome and encouraged to attend.

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