New HRZZ Project at the School of Applied Mathematics and Computer Science

On December 16, 2024, at the School of Applied Mathematics and Informatics, University of Josip Juraj Strossmayer in Osijek, a new research project titled Metric Properties of Graphs (MetGraph) will commence. The project is funded by the Croatian Science Foundation and will run from December 2024 to December 2027.

The project leader is Prof. Dr. Snježana Majstorović Ergotić, supported by a team of distinguished domestic and international scientists: Prof. Dr. Tomislav Došlić and Dr. Luka Podrug from the University of Zagreb, Prof. Dr. Riste Škrekovski from the University of Ljubljana (Slovenia), Prof. Dr. Dragan Stevanović from Abdullah Al Salem University (Kuwait), Prof. Dr. Jelena Sedlar from the University of Split, Dr. Tobias Hofmann from the Technical University of Berlin (Germany), and PhD student Kurt Klement Gottwald from Chemnitz University of Technology (Germany). During the project’s duration, one senior assistant (postdoctoral researcher) and one assistant will be hired.

The project focuses on exploring various problems related to metrics on graphs, which have broad applications in analyzing complex networks, ranging from computer and technological networks to biological, social, and climate systems. The main research areas include the metric properties of graphs and digraphs, covering problems related to vertex distances (graph metrics), their generalizations, extensions, and applications. The project aims to solve numerous open questions related to shortest path distance, resistance distance, Steiner distance, and flow distance, as well as analyzing several types of metric dimensions of graphs. Special attention will be given to studying recently defined families of graphs, such as metallic, Horadam, and Horadam-Lucas cubes. Furthermore, the project includes research into hypotheses from spectral graph theory and the development of heuristic algorithms for calculating certain graph invariants based on graph neural networks (GNNs).

The project aims to develop a coherent, internationally recognized research group that will contribute to advancing scientific knowledge and international collaboration. Additionally, hiring young researchers (an assistant and a postdoctoral researcher) will provide opportunities for educating a new generation of scientists ready to tackle the most challenging research problems.

It should be noted that the MetGraph project stands out as one of the 415 projects submitted for the IP-2024-05 competition. It was approved alongside 42 other projects in the fields of natural and technical sciences, and it is one of only two approved projects in the field of mathematics.

The success of our scientist, Prof. Dr. Snježana Majstorović Ergotić, is even more significant as, in addition to leading the MetGraph project, she recently became a collaborator on two bilateral scientific research projects scheduled for implementation from 2024 to 2026:

• Graphs and Diophantine Equations in Modeling Molecular Structures – a Croatian-Hungarian project; Croatian lead: Tomislav Došlić (University of Zagreb), Hungarian lead: László Németh (University of Sopron).
• On the Research of Induced and Maximal Matchings in Graphs – a Croatian-Chinese project; Croatian lead: Tomislav Došlić (University of Zagreb), Chinese lead: Lingjuan Shi (Northwestern Polytechnical University).

We extend our congratulations to our scientist, Snježana, on this remarkable achievement and the awarded projects!