Projects / Programmes
January 1, 2022
- December 31, 2027
| Code |
Science |
Field |
Subfield |
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| 1.07.00 |
Natural sciences and mathematics |
Computer intensive methods and applications |
|
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
| 1.02 |
Natural Sciences |
Computer and information sciences |
mathematics, graph theory, topological graph theory, metric graph theory, graph products, chemical graph theory, geometric graphs, graph invariants, algorithmic graph theory, applications of graph theory
Data for the last 5 years (citations for the last 10 years) on
June 28, 2024;
A3 for period
2018-2022
| Database |
Linked records |
Citations |
Pure citations |
Average pure citations |
| WoS |
1,047 |
14,771 |
12,462 |
11.9 |
| Scopus |
1,137 |
17,250 |
14,748 |
12.97 |
Researchers (24)
Organisations (2)
Abstract
The research programme of our group is to remain at the forefront of research in the field of graph theory. We will continue researching central, standard areas of graph theory. In addition to that, we intend to be one step ahead of the competition and explore and introduce new concepts, techniques, and applications. Among the areas that we especially plan to develop are domination theory, metric graph theory, graph colorings, chemical graph theory, graph products, hamiltonicity, topological and geometric graph theory, and applications of these areas. A brief summary of some of the problems and topics that we will investigate follows. In domination theory we will investigate the number of optimal sets for domination invariants, the problem of finding the graphs with unique optimal sets, different domination games, and Grundy invariants. In metric graph theory we will focus on the variety of metrically defined subclasses of hypercubes, the Hausdorff distance, the Wiener index of digraphs, and relations of metric graph theory with oriented matroids. We will especially investigate daisy cubes and daisy graphs of rooted graphs, Pell graphs, cube complements of graphs, and a connection between statistical learning and geometric properties of subgraphs of hypercubes. The main themes of graph colorings will be packing and S-packing colorings, and different distance colorings. In chemical graph theory we plan to develop a generalized approach to determine the extremal structures for some degree-based topological indices, investigate resonance graphs, and determine the best performing model for the prediction of physico-chemical properties of unsaturated hydrocarbons. For graph products we plan to study some specific problems and consider in depth properties of the direct-co-direct product and the modular product. For hamiltonicity we will investigate the problem whether Thomassen's result can be improved for (list) colorings of Eulerian triangulations, investigate the problem whether Chvatal's conjecture holds for bipartite graphs and investigate whether all 1-tough bipartite graphs are prism-hamiltonian. In the area of the topological and geometric graph theory we will study the structure of crossing critical graphs, genus and crossings of sparse, dense, and random objects, graph and subgraph isomorphism of geometrically represented graphs, and the use of algebraic techniques in geometric and topological graphs. Along with many of the listed topics, algorithmic aspects will also be investigated.
Significance for science
The programme belongs to basic research in the area of mathematics and related fields such as computer science. Problems that we are solving and posing are internationally important, which can in particular be justified by our bibliography from the last period as well as with the (citation) impact of our results. The bibliography testifies that, on the one hand, we managed to solve many problems, some of which were open for a long time and were (unsuccessfully) tried to be solved by other groups of researchers. On the other hand, we posed several new problems and directions of research, which met with great repercussions in the world; let us mention the theory of the domination game, the concept of the minimum k-path vertex cover, the concept of M-polynomial, the concept of strong geodetic sets, and the general position graph theory problem. Our goal is to continue research in both directions, that is, to solve important open problems and to open new areas of research. The problems are central in the area of graph theory and at the same time have applications in other scientific fields. For instance, our results on carbon nanotubes can accelerate the synthesis of carbon nanomolecules and therefore help the improvement of nanomaterials. Distances between graphs are used in those areas of science where similarities of objects are studied. New insights concerning distances between graphs further develop existing areas and give a fresh look at existing problems, specifically in areas like biology, computer science, chemistry, social sciences and linguistics. The study of graph invariants addresses some important real life problems. In particular, the frequency assignment problem asks for assigning frequencies to transmitters in a wireless network. We expect that the newly obtained results will be published in leading journals from the area of discrete mathematics and we will present them at international scientific conferences. We expect that we will be invited to deliver several invited plenary talks which will further emphasize the importance of our research achievements. In this way we will further increase the international role of the Slovenian graph theory school.
Significance for the country
The project is from the area of pure mathematics, therefore it is difficult to measure its direct impact on the economy and society. However, the research programme is oriented to encourage the integration of the most promising young researchers. In this way it enables a long term continuation of the research quality in mathematics, which in turn has a positive influence on the quality of the university programs in mathematics and other sciences. In the period 2016-2021 we have supervised 5 Ph.D. students from the ARRS Young Researcher Programme, and additional 14 Ph.D. students not funded within the ARRS Young Researcher Programme. After finishing their Ph.D., our students are getting employed also in industry, hence our programme has a positive impact on the national economy. Since mathematics is used in many other areas, the quality of research in mathematics has an indirect but important influence on the development of other disciplines as well. Inside mathematics the programme mostly develops graph theory and keeps and strengthens its world reputation. The expected results are mostly theoretical. Nevertheless, they have a big potential for applications, especially our research in algorithmic and optimization aspects of graph theory. This can be well justified with our previous research that has led to a cooperation with the Slovenian industry focused on technological development, mostly in the information and telecommunication technology. Specifically, we were cofounders of the startup DataBitLab d.o.o. (2018) and participated in Ministry of health consulting group on COVID-19 modelling. We have also acted as mentors of Student Innovation Projects for Social Benefit which resulted in the final form of web applications. Members of the programme were also among the main organisers of the 9th Slovenian international conference on graph theory in 2019, which was with 300+ participant the biggest event in graph theory in 2019. In summary, we have supported a long-term continuation of the research quality in mathematics, which in turn has an important impact on the quality of the university programs in mathematics and other sciences. As a direct impact of the project we can also consider the fact that it supports a continuation of research contacts of Slovenian scientists with the most up-to-date developments. In particular, this includes the cooperation with renowned researchers, who present the worldly recognized Hungarian combinatorial school.
