1-7 July 2018
Rogla, Slovenia
UTC timezone

# Confirmed Invited Speakers:

Francesco Belardo (University of Naples Federico II, Naples, Italy)

Title: Recent developments on the spectral determination of signed graphs

Abstract: The Spectral Determination Problem is one of the oldest problems in Spectral Graph Theory: given a graph, or a class of graphs, are there non-isomorphic graphs whose spectrum, with respect to a given graph matrix (adjacency, Laplacian, etc.), is the same? The literature contains many results on simple graphs. Here, we focus our attention to Signed Graphs, i.e., graphs whose edges get a sign (say, $+1$ or $-1$). The spectral determination problem can be considered for signed graphs as well, and it becomes a even more complicated problem. In this talk, we discuss the difference in studying signed graphs w.r.t. simple graphs and we will survey some recent results in this respect.

Slides.


Shaofei Du (Capital Normal University, Beijing, China)

Title: Lifting techniques in covering graphs and applications

Abstract:  Constructing graphs by voltage assignment (voltage graph) is one of basic tools in algebraic graph theory and topological graph theory.

A key problem for that is to determine the liftings of automorphisms in the underlying graph.

In this talk we shall present some techniques for determining liftings by using lifting theorem and group theory and also show some applications in classifying arc-transitive graphs.

Slides.

Wilfried Imrich (Montanuniversitat Leoben, Leoben, Austria)

Title: Vertex- and edge-transitivity in products of finite and infinite graphs

Slides.

Arnold Neumaier (University of Vienna, Vienna, Austria)

Title: Counting in distance-regular graphs

Abstract: A systematic technique for counting in distance-regular graphs
is introduced. It is applied to give new proofs for a number of
inequalities for the intersection parameters of distance-regular
graphs.

Sanja Rukavina (University of Rijeka, Rijeka, Croatia)

Title: Construction of self-orthogonal linear codes from orbit matrices of combinatorial structures

Abstract: The incidence structures can be presented by their incidence matrices. An automorphism group acting on the structure induces the tactical decomposition of the corresponding incidence matrix, from which one can construct the related orbit matrix.

We will study codes spanned by the rows of an orbit matrix of a symmetric design with respect to an automorphism group that acts with all orbits of the same length. The dimension of such codes will be discussed. We define an extended orbit matrix and show that under certain conditions the rows of the extended orbit matrix span a code that is self-dual with respect to a certain scalar product.

We will also study codes spanned by the rows of the quotient matrices of symmetric (group) divisible designs (SGDD) with the dual property. In a similar way as in the case of symmetric designs, we will discuss self-dual codes constructed from the extended quotient matrices of SGDDs.

In adition, we will present a construction of self-orthogonal linear codes from orbit matrices of strongly regular graphs and show that under certain conditions submatrices of orbit matrices of strongly regular graphs span self-orthogonal codes.

Primož Šparl (University of Ljubljana, Ljubljana, Slovenia)

Title: Some recent results on half-arc-transitivity of graphs

Abstract: Even though most papers on half-arc-transitive graphs (that is vertex-and edge- but not arc-transitive graphs) or graphs admitting such automorphism groups state that the investigation of such graphs originated in 1966 when Tutte proved that such graphs are necessarily of even valence, the theory really started to develop at the end of the 20th century. In the last 20 years several dozens of papers on these graphs have been published with more and more different researchers becoming interested in the topic. While the majority of papers deals with half-arc-transitive graphs of the smallest possible valence recent years brought some progress also for valences $6$ and more.

In this talk I will present some of my favorite topics in the study of graphs admitting half-arc-transitive group actions and will give an overview of some recent (and perhaps not so very recent) results on such graphs, some for valence 4 and some for higher valences.

Paul Terwilliger (University of Wisconsin–Madison, Madison, United States)

Title: An infinite-dimensional $square_q$-module obtained from  the $q$-shuffle algebra  for affine $mathfrak{sl}_2$