Univerza na Primorskem Fakulteta za matematiko, naravoslovje in informacijske tehnologije
SI | EN

Raziskovalni matematični seminar - Arhiv

2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010
1 2 3 4 5 6 7 8 9 10 11 12
Datum in ura / Date and time: 18.4.16
(10:00-11:00)
Predavalnica / Location: FAMNIT-POŠTA
Predavatelj / Lecturer: Bettina Eick (Institut Computational Mathematics, Fachbereich Mathematik und Informatik, Technische Universität Braunschweig, Germany)
Naslov / Title: On the classification of groups of prime-power order
Vsebina / Abstract:

This talk gives a survey on the state of the art in the classification of the finite groups of prime-power order. Given a prime p and a natural number n, one can consider the function f(p,n) of groups of order p^n (up to isomorphism). The function f(p,n) can be considered as a function in p or as a function in n and then has different interesting asymptotic properties. However, using the order is not the only way to approach the classification of groups of prime-power order. An alternative approach is to classify the groups of prime-power order using their coclass as primary invariant. The talk will explain this in more detail and also exhibit some of the results of this approach.


Datum in ura / Date and time: 18.4.16
(11:00-12:00)
Predavalnica / Location: FAMNIT-POŠTA
Predavatelj / Lecturer: Slobodan Filipovski (UP IAM, UP FAMNIT)
Naslov / Title: On the excess of vertex-transitive graphs of given degree and girth
Vsebina / Abstract:

We consider the problem of finding the smallest vertex-transitive k-regular graphs of girth g. Counting cycles and using number theory's theorems we extend Biggs's result proving that the asymptotic density of the set of all odd girths g for which exists a vertex-transitive (k,g)-cage with excess not exceeding e is 0. Also, we consider the existence of (k,g)-vertex-transitive graphs when g is even and the excess is 4 or smaller than min{k-2,g}.

Based on joint work with Robert Jajcay.


Datum in ura / Date and time: 11.4.16
(10:00-11:00)
Predavalnica / Location: FAMNIT-POŠTA
Predavatelj / Lecturer: Matjaž Krnc (UP FAMNIT, UP IAM)
Naslov / Title: Kronecker covers and generalized Petersen graphs
Vsebina / Abstract:

The family of generalized Petersen graphs G(n,k), introduced by Coxter et al. (1950) and named by Mark Watkins (1969), is a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. The Kronecker cover of a simple undirected graph G  is a a special type of bipartite covering graph of G, isomorphic to the direct (tensor) product of G and K_{2}. In the seminar we will identify generalized Petersen graphs G(n,k) that are Kronecker covers of another generalized Petersen graphs, and discuss some related questions.