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Projects / Programmes source: ARIS

Algebraic Graph Theory with Applications

Research activity

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 
Keywords
covering techniques, transitive group action, representation of transitive groups, (directed) strongly regular graph, distance-regular graph, Schur ring, Boolean function
Evaluation (rules)
source: COBISS
Researchers (24)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  01467  PhD Vladimir Batagelj  Mathematics  Researcher  2016 - 2017  978 
2.  33231  PhD Katja Berčič  Mathematics  Researcher  2015 - 2016  24 
3.  33987  PhD Monika Cerinšek  Computer intensive methods and applications  Researcher  2015 - 2016  21 
4.  34109  PhD Edward Tauscher Dobson  Mathematics  Researcher  2014 - 2017  74 
5.  37724  PhD Robert Jajcay  Mathematics  Researcher  2016 - 2017  54 
6.  35727  Olga Kaliada    Technical associate  2014 - 2016 
7.  34750  PhD Gašper Košmrlj  Mathematics  Researcher  2015  19 
8.  25997  PhD Istvan Kovacs  Mathematics  Researcher  2014 - 2017  215 
9.  34751  PhD Boštjan Kovač  Mathematics  Researcher  2015  10 
10.  24997  PhD Klavdija Kutnar  Mathematics  Researcher  2014 - 2017  254 
11.  23501  PhD Boštjan Kuzman  Mathematics  Researcher  2014 - 2017  265 
12.  02507  PhD Aleksander Malnič  Mathematics  Researcher  2014 - 2017  252 
13.  02887  PhD Dragan Marušič  Mathematics  Head  2014 - 2017  600 
14.  21656  PhD Štefko Miklavič  Mathematics  Researcher  2014 - 2017  201 
15.  30211  PhD Martin Milanič  Mathematics  Researcher  2014 - 2017  313 
16.  27777  PhD Enes Pasalic  Mathematics  Researcher  2014 - 2017  138 
17.  01941  PhD Tomaž Pisanski  Mathematics  Researcher  2014 - 2017  866 
18.  18838  PhD Primož Potočnik  Mathematics  Researcher  2014 - 2016  239 
19.  32026  PhD Rok Požar  Mathematics  Researcher  2016 - 2017  43 
20.  29820  PhD Dragan Stevanović  Mathematics  Researcher  2014 - 2016  135 
21.  17808  PhD Rok Strašek  Mathematics  Researcher  2016 - 2017  142 
22.  23341  PhD Primož Šparl  Mathematics  Researcher  2014 - 2017  194 
23.  34799  Viljem Tisnikar  Mathematics  Researcher  2016 - 2017 
24.  28586  PhD Gabriel Verret  Mathematics  Researcher  2014 - 2016  63 
Organisations (3)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0588  University of Ljubljana, Faculty of Education  Ljubljana  1627082  30,839 
2.  1669  University of Primorska, Andrej Marušič Insitute  Koper  1810014007  10,879 
3.  2790  University of Primorska, Faculty of mathematics, Natural Sciences and Information Technologies  Koper  1810014009  17,883 
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
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