This work is an attempt to establish a stronger link between mathematics and chemistry and also to introduce discrete structures, e. g. maps, into the field of mathematical chemistry. We present the Hückel Molecular-Orbital theory and focus our attention to the notion of free valence. It is assumed in the literature that the maximum $\pi$ bond number (i.e., the total $\pi$ bond order around a $sp^2$ carbon atom) that can be theoretically obtained (on any centre in any $sp^2$ $\pi$ system) is no larger than $\sqrt{3}$. This statement does not appear to have been formally proved. We obtained some partial results. We also provide empirical evidence on the behaviour of maximum $\pi$ bond number as a function of vertex count, $n$, of chemical graphs and describe the family of graphs that realises local maxima for small $n$. In 2013, a group of scientists led by Roman Jerala successfully designed a self-assembled tetrahedral polypeptide. We describe a suitable mathematical model for self-assembly of polypeptide structures. We also provide a dynamic programming algorithm for enumeration of strong traces, i. e., double traces of a graph that have additional properties. In 2012 the interesting family of convex benzenoids was introduced by Cruz et al. We present several equivalent definitions of convex benzenoids and explain some of their properties. In OEIS the sequence A116513 by A. C. Wechsler represents their enumeration. S. Reynolds enumerated and listed them all up to 250 hexagons. Our study independently verifies their enumeration. Furthermore, we stratify their generation into what we call the fundamental families of convex benzenoids. We provide an algorithm which extends the table up to $10^6$ hexagons. In this work we also revisit coronoids, in particular multiple coronoids. We consider a mathematical formalisation of the theory of coronoid hydrocarbons that is solely based on incidence between hexagons of the infinite hexagonal grid in the plane. We also consider perforated patches, which generalise coronoids: in addition to the hexagons of any benzenoid, other polygons may also be present. Just as coronoids may be considered as benzenoids with holes, perforated patches are patches with holes. Both cases, coronoids and perforated patches, admit a generalisation of the altan operation that can be performed at several holes simultaneously. A formula for the number of Kekulé structures of a generalised altan can be derived easily if the number of Kekulé structures is known for the original graph. Pauling bond brders for generalised altans are also easy to derive from those of the original graph.
D.09 Tutoring for postgraduate students
COBISS.SI-ID: 17740889Dragan Marušič, Klavdija Kutnar and Tomaž Pisanski are Editors-in-Chief of the International mathematical journal ‘Ars Mathematica Contemporanea’ covered by Math. Reviews (indexed cover-to-cover), Zentralblatt MATH, COBISS, SCOPUS, Science Citation Index-Expanded (SCIE), Web of Science, ISI Alerting Service, and Current Contents/Physical, Chemical & Earth Sciences (CC/PC & ES). With this journal Slovenian mathematics has opened a new chapter in its development and has definitely put itself on the world map. In addition, some of other project members are members of Editorial board of this journal. Some of the project members are also founding editors of the scientific journal The Art of Discrete and Applied Mathematics established in 2017 with the first issue published in 2018. Tamas Szonyi (HU leader of this project) is a member of the Editorial Board of this new journal.
C.04 Editorial board of an international magazine
COBISS.SI-ID: 239049984Tomaž Pisanski is chairing organizing committee of the 8th European Congress of Mathematics which will be held in Slovenia in 2020. Several other members of the project (Klavdija Kutnar - deputy chair, Ademir Hujdurović, Edward Dobson, Dragan Marušič - local scientific committe chair, Martin Milanič) are included into the organization of the congress. HU leader of this project is also a member of the organizing committee. European Congress of Mathematics is the second largest mathematical event in the world, after the International Congress of Mathematics and is organized every 4 years. More than 1,000 mathematicians usually take part in it. Based on the candidature the organization of the 8th congress was given to Slovenia by the Council of the European Mathematical Society in June 2016. The candidature was launched by UP FAMNIT in collaboration with UP IAM, UL FMF, UL PEF, UM FNM and all other organisations active in the field of mathematics in Slovenia, while it was supported also by the MIZŠ, ARRS, SAZU and Slovenian Rectors' Conference.
B.01 Organiser of a scientific meeting