Projects / Programmes
Application of semiregular group actions in some open problems in algebraic graph theory
| Code |
Science |
Field |
Subfield |
| 1.01.04 |
Natural sciences and mathematics |
Mathematics |
Algebra |
| Code |
Science |
Field |
| P110 |
Natural sciences and mathematics |
Mathematical logic, set theory, combinatories |
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
graph, automorphism group, semiregular automorphism, Hamilton cycle, Cayley graph, strongly regular (di)graph
Researchers (15)
Organisations (2)
Abstract
This project proposal is a natural follow up of the research project J1-2055 On the problem of existence of semiregular elements in 2-closed transitive groups with application in vertex-transitive graphs funded by Slovenian Research Agency (ARRS). The project J1-2055 was a three-year project which successfully ended in April 2012. It consisted of six researchers producing 54 original scientific papers published in SCI journals, of which 2 in SCI journals ranking A'', and 10 in SCI journals ranking A' (according to ARRS methodology). For detailed information about this project see http://izumbib.izum.si/bibliografije/J20120525113842-J1-2055.html.
The motivation comes from an open problem, posed in 1981, when the project proposal leader (D. Marušič, On vertex symmetric digraphs, Discrete Math. 36 (1981), 69-81) asked if it is true that every vertex-transitive graph has a semiregular automorphism. This problem was later generalized to 2-closed transitive permutation groups (P.J. Cameron (Ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167/168 (1997), 605–615). In spite of increasing efforts (regarding this problem) resulting in a number of partial positive results in the course over the last ten years, it seems that we still have a long way to go. The proposed project will involve work on various aspects of this problem, with applications to other open problems in algebraic graph theory.
Significance for science
Apart from Art, Mathematics is the only universal language of human communication present in all civilizations. Abstract mathematical theories are used in Natural Sciences, Engineering, Computer Science and also in Social, Economic and Biomedical Sciences. It has an essential role in many important areas of research, such as Safe Communications, Data Protection, or Decoding of Humane Genome, thus proving that its influence to the very foundations of modern society has reached previously unthinkable levels. The project was at the cutting edge of today's research in Algebraic Graph Theory (AGT) and its multidisciplinary applications to other sciences. The importance of our research goals and results can be seen from project team members’ bibliographies, their citations, and numerous links with scientists around the world.
Significance for the country
These stormy times of social changes call for an even tighter incorporation of Mathematics into scientific research and education thus enabling a faster technological development in Slovenia. Our group already has many experiences in this field. The program group is included into a grant awarded by the European Commission under the Horizon 2020 Teaming grant instrument. The purpose of the funds (45 million EUR) is to increase innovation excellence in Europe in general, especially in member states underperforming in innovation (EU13). Our existence as a fully developed nation in Europe depends as much on preserving our language and culture as it depends on having a highly educated population. It is thus necessary to be able to use different communication channels – and mathematics, as a universal language, is a key factor here.
Most important scientific results
Annual report
2013,
2014,
2015,
final report
Most important socioeconomically and culturally relevant results
Annual report
2013,
2014,
2015,
final report
