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Bilateral Research Project Slovenia - Hungary N1-0140
Geometries, Graphs, Groups and their Links


Project Title: Geometries, Graphs, Groups and their Links

PI: Istvan Kovacs

Project Code: N1-0140

Type of the Project: bilateral research project Slovenia - Hungary.

Funding Organization: Slovenian Research Agency (ARRS) and Hungarian Research Agency.

Research Field (ARRS): 1.01.00 - Natural Sciences and Mathematics / Mathematics.

Duration: 1. 3. 2020 - 28. 2. 2023.

Project Category: B.

Yearly Range: 0.43 FTE (734 research hours).

Sicris profile of the project is avaliable here.

Research Organizations:
University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies

Project Members:

Basić Nino (ARRS šifra: 34561)
Dobson Edward Tauscher (ARRS šifra: 34109)
Hujdurović Ademir (ARRS šifra: 32518)
Kovacs Istvan (vodja) (ARRS šifra: 25997)
Kutnar Klavdija (vodja, ARRS šifra: 24997)
Marušič Dragan (ARRS šifra: 02887)
Miklavič Štefko (ARRS šifra: 21656)
Orel Marko (ARRS šifra: 25610)
Pisanski Tomaž (ARRS šifra: 01941)


The Hungarian research group is mostly located at ELTE and the MTA-ELTE Geometric and Algebraic Combinatorics Research Group and the Slovenian research group is mostly located at University of Primorska. The cooperation of this research group with our Slovenian colleagues has started in the end of 1990s. Since then several visits have taken place in both directions in the framework of Slovenian-Hungarian Intergovernmental Scientific and Technological Projects. The focus was always on algebraic methods applied to graph theory and (finite) geometry. Since 2015 we have been cooperating on similar topics in the framework of an OTKA-ARRS project. This collaboration led to several joint papers and we had fruitful discussions about many other papers. The present proposal is natural continuation of our joint work. We also have a cooperation in teaching: University of Primorska and Eötvös Loránd University have an active Erasmus agreement. Besides the eight Hungarian and nine Slovenian colleagues, we also plan to work closely with Gábor Korchmáros (Potenza, Italy), who has a deep knowledge in group theory and geometry, and their application to graph theory. In particular, he wrote several papers on automorhism groups of graphs and geometries.

In the present project we would like to continue and strengthen our cooperation in the use of algebraic, geometric, and combinatorial techniques for problems about graphs, groups, configurations and geometries. In some cases the current topics grew out of our work in the previous OTKA-ARRS project. From a distance, the topics and the aims did not change, we would like to attack problems which reveal connections between geometris, graphs and groups. In a sense, this is also the aim of the Slovenian journals Ars Math. Contemporanea and Art of Discrete and Applied Maths. Of course, the concrete problems are different. We plan to use this project to support exchange of Ph.D. students, in particular, we plan to organize workshops to spread the results obtained in the project.

We have the following specific topics on which we plan to work on: Configurations; Graphs and groups from quadratic forms over finite fields; Distance-regular Cayley graphs; Edge-girth regular graphs; Frobenius graphical and digraphical representations; CI-property of graphs and geometries; Cores and finite geometry. It should be noted that the above list is necessarily not the full list of problems that we wish to attack together. During our research (many) other problems related to graphs, groups, configurations and geometries may occur.