Prof.
Paul Terwilliger
(U. Wisconsin Madison)
For a $Q$-polynomial distance-regular graph of $q$-Racah type,
the adjacency matrix $A$ and dual adjacency matrix $A^*$ satisfy
the $q$-Dolan/Grady relations. These are the defining relations
for the $q$-Onsager algebra. In this talk we describe how
the $q$-Onsager algebra is related to the positive part of the quantum algebra $U_q(\mathfrak{\widehat sl}_2)$.
Prof.
Marston Conder
(University of Auckland)
Locally-finite vertex-transitive graphs may be classified according
to the action of the automorphism group on the arcs (ordered edges) of the graph.
Let $X$ be vertex-transitive graph of valency $d$, with full
automorphism group $A$. Then the {\em arc-type\/} of $X$ is defined in terms
of the lengths of the orbits of the action of the stabiliser $A_v$ of a
given vertex $v$ on...
Dr
Doris Dumičić Danilović
(Department of Mathematics, University of Rijeka)
In this talk we will describe a method for the construction of block designs admitting a solvable automorphism group using tactical decomposition.
The first step is the construction of mutually nonisomorphic orbit matrices for arbitrary block design and its persumed automorphism group, which is the generalization of the algorithm for obtaining orbit matrices for some symmetric design and its...
Prof.
Tomaž Pisanksi
(University of Primorska)
We may distinguish between two $d$-valent vertex-transitive graphs if they have different arc-types, defined in Marston Conder's talk. Let $t(d)$ denote the number of distinct arc-types for $d$-valent vertex-transitive graphs. We present the generating function for $t(d)$ and explain some of its properties.
Marina Šimac
(Department of Mathematics - University of Rijeka)
The main subject of this talk is the construction of low-density parity-check (LDPC) codes based on the adjacency matrix of $\mu$-geodetic graphs obtained from block designs. We will discuss some properties of obtained codes, especially of LDPC codes constructed from $\mu$-geodetic graphs obtained from block designs with $k=3$.
This is a joint work with Sanja Rukavina.
Dr
Marija Maksimović
(Department of Mathematics - University of Rijeka)
The subject of the talk is a construction of orbit matrices of strongly regular graphs under the action of an assumed automorphism group and construction of strongly regular graphs and self-orthogonal codes obtained from orbit matrices. The obtained results are the generalization of an algorithm for constructing orbit matrices of strongly regular graphs under the action of the automorphism...
Dr
Sara Sabrina Zemljic
(Science Institute, University of Iceland)
Sierpinski graphs are a two-parametric family of graphs which has been studied in various areas in mathematics and elsewhere. Due to their close relation to the problem of the Tower of Hanoi puzzle, we are mainly interested in distances in Sierpinski graphs. In order to get more information on (metric) properties, we also started studying an algebraic view of these graphs. In the talk I will...
Dr
JianBing Liu
(Department of Mathematics, Beijing Jiaotong University)
In this talk, we calculate the number of isomorphism classes of regular coverings of graph $G$ when the covering transformation groups are $mathbb{Z}_2$-extensions of a cyclic $p$-group.
This is a joint work with Jaeun Lee and Jin Ho Kwak.
Nina Mostarac
(Department of Mathematics - University of Rijeka)
In this talk we will look at codes spanned by the rows of a quotient matrix of a symmetric (group) divisible design (SGDD) with the dual property. We will define an extended quotient matrix and see that under certain conditions the rows of the extended quotient matrix span a self-dual code with respect to a certain scalar product. We will also see that sometimes a chain of codes can be used...
