# 2015 PhD Summer School in Discrete Mathematics

from 27 June 2015 to 3 July 2015
Rogla, Slovenia
UTC timezone
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## Contribution List

Displaying 15 contributions out of 15
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 $U_q(\mathfrak{\widehat sl}_2)$.
Presented by Prof. Paul TERWILLIGER
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 the se ... More
Presented by Prof. Marston CONDER
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 aut ... More
Presented by Dr. Doris DUMIČIĆ DANILOVIĆ
In the setting of Riemannian manifolds, the curvature of the manifold reveals a great deal of information on the spectrum of the Laplace-Beltrami operator. In this talk, we give describe some analogous results in the graph setting, for an appropriate notion of curvature. Among others, we give an analogue to Buser's inequality for graph (which complements Cheeger's inequality, showing that the no ... More
Presented by Prof. Paul HORN
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.
Presented by Prof. Tomaž PISANKSI
In 2013, Gradišar et al. presented a strategy to assemble a single-chain polypeptide tetrahedron from concatenated segments that form coiled-coils. A paper by Klavžar and Rus developed the underlying mathematical model, i.e. introduced stable traces. In 2014, the notion of strong trace was introduced by Fijavž, Pisanski and Rus. It is a refined mathematical model for self-assembly of polypeptid ... More
Presented by Mr. Nino BAŠIĆ
We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identified. ... More
Presented by Sandra KIEFER
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.
Presented by Marina ŠIMAC
Let W_{n,k} be the graph of order nk + 1 and size n(k + 1) obtained from the wheel W_n = K_1+ C_n by subdividing each edge of C_n by k−1 vertices. In [Bull. Math. Soc. Sci. Math. Roumanie 4, 50(2007), 371-376] it was shown that the metric dimension of W_{n,2} denoted by dim(W_n,2), is equal to ⌊2n/3⌋ for every n ≥ 4. In this paper it is shown that dim(W_n,k) is equal to: ⌊n/2⌋ for ... More
Presented by Dr. ayesha RIASAT
We say that a $k$-regular graph of order $v$ is $(v,k,\lambda,\mu)$ strongly regular if any pair of adjacent vertices shares $\lambda$ vertices while non-adjacent vertices share $\mu$ common neighbors. In this talk we will present an approach that will give a full classification of $(75,32,10,16)$ strongly-regular graphs. The main idea is to use the so-called star-complement technique.
Presented by Mr. Jernej AZARIJA
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 group ... More
Presented by Dr. Marija MAKSIMOVIĆ
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 prese ... More
Presented by Dr. Sara Sabrina ZEMLJIC
In this talk, we aim to consider maps and hypermaps whose automorphism group contains a subgroup which acts regularly on vertex set. These maps and hypermaps are called (unoriented) Cayley maps and Cayley hypermaps. We consider some descriptions and properties of these maps and hypermaps. Furthermore, some conditions for these maps and hypermaps to be regular will be dealt with.
Presented by Dr. Young Soo KWON
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.
Presented by Dr. JianBing LIU
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 to as ... More
Presented by Nina MOSTARAC