Prof.
Dragan Stevanovic
(University of Primorska)
We show that a simple expression, that employs a single square root and integer division, yields a surprisingly good estimate of the largest eigenvalue of adjacency matrix of a graph.
Prof.
Paul Fabel
(Mississippi State University)
It is a well established but highly nontrivial fact that planar sets are aspherical (Zastow, Cannon/Conner/Zastrow ).
We discuss another relatively simple and canonical strategy to prove planar sets are aspherical, employing projections
of Hadamard spaces, realized as universal covers of PL planar compacta.
Prof.
Mihael Perman
(University of Ljubljana and University of Primorska)
The Chinese restaurant process is a way to create random premutations that are not equally likely.
One can associate a random measure to the process and examine the limiting behaviour of this
random measure which gives asymptotic information on the structure of cycles.
Dr
Jasna Prezelj Perman
(University of Primorska and University of Ljubljana)
One of the big difficulties in compex analysis is construction of globally defined mappings on complex manifolds. Compact manifolds only have trivial mappings (into $\Cc^n$) and on the other side Stein manifolds have plenty. The next class with a large family of mappings are 1-convex manifolds. In particular, we are interested in constructing mappings with polynomial growth at the boundary in...
Alexander Vasilyev
(University of Primorska)
Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example
in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their
chemical structure.
The set of 148 discrete Adriatic indices...
Prof.
Dragan Marušič
(University of Primorska)
I first met Aleksander Malni\v c in the Spring of 1972 when we were both part of the Slovenian National team at the Yugoslavian Mathematical Olympiad. In this talk I will be reminiscing about our intersecting mathematical paths, our ups and downs, and my joy for the privilege to have been around such a brilliant but yet humble mathematician.
Prof.
Gyorgy Kiss
(Eötvös Loránd University)
A decomposition of a simple graph G=(V(G),E(G)) is a pair
$[G,\mathcal{D}]$
where $\mathcal{D}$ is a set of induced subgraphs of $G$,
such that every edge of $G$ belongs to exactly one subgraph in $\mathcal{D}$.
A \emph{coloring} of a decomposition $[G,\mathcal{D}]$ with $k$ colors
is a surjective function that assigns to edges of $G$ a color from
a $k$-set of colors, such that all...
Prof.
Ted Dobson
(Mississippi State University and University of Primorska)
We show that for certain integers $n$, the problem of whether or not a circulant digraph $\Gamma$ of order $n$ is also isomorphic to a Cayley digraph of some other abelian group $G$ of order $n$ reduces to the question of whether or not a natural subgroup of the full automorphism group contains more than one regular abelian group up to isomorphism (as opposed to the full automorphism group). ...
Prof.
Bojan Kuzma
(University of Primorska)
A commutating graph of an algebra is a simple graph, where vertices are
all noncentral elements of the algebra, and two vertices are connected if
the corresponding elements commute. We will present some problems that are studied in relation to commuting graph.
Prof.
Russ Woodroofe
(Mississippi State University)
Castelnuovo-Mumford regularity is an important graph invariant
in combinatorial commutative algebra. I'll give a definition of regularity
in terms of simplicial homology, which will make it clear that it is a
measure of complexity of a graph. I'll then relate regularity to other
graph invariants.
Prof.
Tomaz Pisanski
(University of Ljubljana and University of Primorska)
Configurations of points and lines have Levi graphs that are well understood. These graphs are bipartite, semi-regular and have girth at least six. They reflect the property that the dual of a configuration of points and lines is again a configuration of points and lines. In case of configurations of points and circles the situation is quite different. For instance, the duality does not...
Dr
Ademir Hujdurovic
(University of Primorska)
A {\it CIS} graph is a graph in which every maximal stable set and every maximal clique intersect.
A {\em well-covered} graph is a graph in which
all maximal stable sets are of the same size,
and {\em co-well-covered} if its complement is well-covered.
A {\it circulant} is a Cayley graph of a cyclic group.
A graph is said to be {\it vertex-transitive} if for every two vertices $u$ and...
Dr
Gabor Gevay
(Bolyai Institute, University of Szeged)
Zonohedra (or more generally, zonotopes) are a particular class of convex polytopes characterized by the property that all their 2-dimensional faces are centrally symmetric. We introduce a generalization of the graph of zonotopes, which we call a zonograph\/.
We show through examples how zonographs can be used in the construction of $(n_k)$ configurations of points and circles. Zonographs...
