18-21 June 2015

Kranjska Gora, Slovenia

Europe/Ljubljana timezone

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Type: Oral presentation

In this talk we present the topological chirality of knots and graphs and discuss its application in chemistry. As a powerful tool ＨＯＭＦＬＹ polynomial of knots are introduced.

Presented by Prof. Fuji ZHANG

Type: Oral presentation

It was conjectured in litearature that the inequality
$\frac{M_{1}(G)}{n}\leq\frac{M_{2}(G)}{m}$ holds for all simple graphs, where
$M_{1}(G)$ and $M_{2}(G)$ are the first and the second Zagreb index. By
further research it was proven that the inequality holds for several graph
classes such as chemical graphs, trees, unicyclic graphs and subdivided
graphs, but that generally it does not hold
... More

Presented by Dr. Jelena SEDLAR

Type: Oral presentation

The concept of conjugated circuits is revisited from a mathematical stand-point. Some classical results are explained and some applications and computations involving iterated altans, ring currents, and resonance graphs are presented.

Presented by Prof. Tomaž PISANSKI

Type: Oral presentation

A matching $M$ in a graph $G$ is maximal if it cannot be extended to a larger matching in $G$. In this paper we show how several chemical and technical problems can be successfully modeled in terms of maximal matchings. Then we enumerate maximal matchings in several classes of graphs made by a linear or cyclic concatenation of basic building blocs. We also count maximal matchings in joins and coro
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Presented by Prof. Tomislav DOšLIć

Type: Oral presentation

The concepts of assortative and dissortative mixing in complex networks are important concepts that gives us an insight in the network robustness, infection spreading on networks, its temporal and other properties. In this paper, we define descriptors that enable us to refine these concepts thus giving us a better insight in network properties. Moreover, we transfer the knowledge obtained from thi
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Presented by Prof. Damir VUKIčEVIć

Type: Oral presentation

Proteins as the central molecules of life fold into versatile compact tertiary structures defined by a large number of cooperative weak long range interactions, which are very difficult to predict and even more to design. DNA-based nanostructures can represent an inspiration for the design of new protein folds. In comparison to DNA, polypeptide coiled-coil dimers can form both parallel and antipar
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Presented by Dr. Ajasja LJUBETIč, Prof. Tomaž PISANSKI

Type: Oral presentation

The edge-Wiener index of a graph $G$ is defined as the Wiener index of the line graph of $G$. An algorithm will be presented that, for a given benzenoid system $G$ with $m$ edges, computes the edge-Wiener index of $G$ in $O(m)$ time. The key to the algorithm is a reduction of the problem to three different weighted trees. In addition to the previously used weighted vertex- and edge-Wiener indices,
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Presented by Prof. Sandi KLAVžAR

Type: Oral presentation

Protein alignment

Presented by Prof. Milan RANDIć

Type: Oral presentation

The chemically important interrelations between discrete and continuous models of molecules and molecular fragments, such as functional groups, have received considerable attention recently. Some of the relations, discovered long ago, can be extended within a novel framework that allows the application of a wider range of mathematical tools, especially, those of algebraic and differential topology
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Presented by Prof. Paul MEZEY

Type: Oral presentation

A {\em fullerene graph} is the molecular graph of a carbon fullerene molecule, whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds between pairs of atoms. In mathematics, a fullerene graph is a planar (or spherical) cubic graph with exactly 12 pentagonal faces and other hexagonal faces. The Clar number of a fullerene graph is the maximum number of mutuall
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Presented by Prof. Heping ZHANG

Type: Oral presentation

In our attempt to classify the tilings of the sphere by geometrically congruent pentagons, we need to understand the topological aspects by ignoring the edge lengths and angles. This means the study of the embedded graph such that each cell is a pentagon. We find that most vertices should have degree 3, and the distribution of the vertices of degree > 3 has implications on the graph. Besides the a
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Presented by Prof. Min YAN

Type: Oral presentation

Carbon nanotubes were discovered almost 30 years ago and their unique structure explains their unusual properties such as conductivity and strength. Their aromaticity can be mathematical modeled with resonance graphs, where vertices are perfect matchings t.i. Kekule structures of a nanotube, and two vertices are adjacent, if their symmetric difference is a hexagon.
Lucas cubes are a class o
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Presented by Prof. Petra ŽIGERT PLETERšEK

Type: Oral presentation

A fullerene is a plane trivalent graph with pentagonal and hexagonal faces and is designed to model carbon molecules. The Fries number is the maximum number of benzene faces, or conjugated 6-circuits. The Clar number is the maximum number of independent benzene faces. These two parameters are linked to the stability of the molecule. We will discuss the structure of a fullerene with respect to
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Presented by Dr. Elizabeth HARTUNG

Type: Oral presentation

In chemistry and physics, the passage of time results in the increase of entropy of the universe – so that entropy is sometimes referred to as the “arrow of time”. Entropy, however, is also commonly associated with disorder so that biological evolution seems contrary since ecosystem order (or complexity) often (but not always) seems to increase through time. In this lecture we explore an e
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Presented by Prof. William SEITZ

Type: Oral presentation

In this talk we will introduce the concept of Steiner
Wiener index for a (molecular) graph. Some basic mathematical
results are obtained, and a chemical application is reported.
This is a joint work with Y. Mao, I. Gutman and B. Furtula.

Presented by Prof. Xueliang LI

Type: Oral presentation

The Wiener index has been generalized in many ways, some by considering distance between edges, and others
by counting some special types of vertex distances. Graovac and Pisanski \cite{1}, presented an algebraic modification of the Wiener index of a graph by considering its symmetry group. To explain,
we assume that $G$ is a graph with automorphism group $\Gamma =
Aut(G)$. Define the {\it dist
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Presented by Prof. Ali ASHRAFI