Projects / Programmes
Algebraic Graph Theory with Applications
| Code |
Science |
Field |
Subfield |
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| Code |
Science |
Field |
| P001 |
Natural sciences and mathematics |
Mathematics |
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
covering techniques, transitive group action, representation of transitive groups,
(directed) strongly regular graph, distance-regular graph, Schur ring, Boolean function
Researchers (24)
Organisations (3)
Abstract
In the past 30 years, Algebraic Graph Theory (AGT) has arisen as one of the main areas of contemporary scientific research in mathematics. While its rapid development is partially due to increasing importance of technology and networks, it was a number of original and valuable contributions by distinguished researchers that established AGT as a mature mathematical discipline. Over the years the Slovenian School of AGT has been an essential part of the development of AGT on the global level. Its international recognition has attained levels comparable to those reached by similar institutions from the technologically most developed countries around the world.
This project proposal is a natural follow up of the basic research project J1-4021 Algebraic Graph Theory and Applications (2011-2014) led by Dragan Marušič, which is going to end in June 2014 with many important new contributions to the field. It concentrates on some of the most relevant research areas within AGT: Covering techniques, construction of catalogues, and algorithmic aspects; the study of representations of transitive groups on eigenspaces of the adjacency matrix of a given graph; the construction of (directed) strongly regular graphs admitting particular symmetry properties; the study of a certain type of bipartite distance-regular graphs; the study of graphs admitting particular group actions, such as: graphs admitting an arc-transitive group of automorphisms with a non-semi-regular abelian normal subgroup, k-flows in graphs admitting vertex-transitive group actions, graphs admitting long consistent cycles; non-schurian S-rings which form a link between the abstract group theory and algebraic combinatorics, and the separability problem of S-rings over cyclic groups together with applications to AGT and finite geometry; and the study of correspondence between AGT and cryptology.
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
2014,
2015,
final report
Most important socioeconomically and culturally relevant results
Annual report
2014,
2015,
final report
