Raziskovalni matematični seminar
Raziskovalni matematični seminar poteka v organizaciji oddelkov za matematiko dveh članic Univerze na Primorskem - UP FAMNIT in Inštituta Andrej Marušič (UP IAM), in sicer vsak ponedeljek od oktobra do junija.
Vljudno vabljeni k udeležbi na prihodnjih seminarjih!
Datum in ura / Date and time: 9.12.24
(15:00-16:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Safet Penjić (University of Primorska)
Naslov / Title: On combinatorial structure and algebraic properties of certain family of (di)graphs obtained from normal irreducible nonnegative matrices
Vsebina / Abstract:
Let B\in Mat_X(R) denote a normal irreducible nonnegative matrix, and B={p(B) | p\in C[t]} denote the vector space over C of all polynomials in B. For the moment let us define a 01-matrix A in the following way: (A)_{xy}=1 if and only if (B)_{xy}>0 (x,y\in X). Let Γ=Γ(A) denote a (di)graph with adjacency matrix A, diameter D, and let A_D denote the distance-D matrix of Γ. In this talk we show that B is the Bose--Mesner algebra of a commutative D-class association scheme if and only if B is a normal λ-doubly stochastic matrix with D+1 distinct eigenvalues and A_D is a polynomial in B.
This is a work in progress, and the preprint is available at https://arxiv.org/abs/2403.00652
It is a joint work with Giusy Monzillo.
Let X denote a nonempty finite set. A nonnegative matrix B\in Mat_X(R) is called λ-doubly stochastic if
∑_{z\in X}(B)_{yz} = ∑_{z\inX}(B)_{zy}=λ for each y\in X.
Let B\in Mat_X(R) denote a normal irreducible nonnegative matrix, and B={p(B) | p\in C[t]} denote the vector space over C of all polynomials in B. For the moment let us define a 01-matrix A in the following way: (A)_{xy}=1 if and only if (B)_{xy}>0 (x,y\in X). Let Γ=Γ(A) denote a (di)graph with adjacency matrix A, diameter D, and let A_D denote the distance-D matrix of Γ. In this talk we show that B is the Bose--Mesner algebra of a commutative D-class association scheme if and only if B is a normal λ-doubly stochastic matrix with D+1 distinct eigenvalues and A_D is a polynomial in B.
This is a work in progress, and the preprint is available at https://arxiv.org/abs/2403.00652
It is a joint work with Giusy Monzillo.
