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Projects / Programmes source: ARIS

Algebraic Graph Theory and Applications

Research activity

Code Science Field Subfield
1.01.05  Natural sciences and mathematics  Mathematics  Graph theory 

Code Science Field
P110  Natural sciences and mathematics  Mathematical logic, set theory, combinatories 

Code Science Field
1.01  Natural Sciences  Mathematics 
Keywords
graph, vertex-transitive, edge-transitive, arc-transitive, Cayley graph, transitive permutation group, (im)primitivity, graph cover, Schur ring, coherent configuration, association scheme, CI-group.
Evaluation (rules)
source: COBISS
Researchers (15)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  24999  PhD Boštjan Frelih  Mathematics  Researcher  2011 - 2014  14 
2.  20269  PhD Iztok Kavkler  Mathematics  Researcher  2011 - 2014  59 
3.  25997  PhD Istvan Kovacs  Mathematics  Researcher  2011 - 2014  215 
4.  23501  PhD Boštjan Kuzman  Mathematics  Researcher  2011 - 2014  265 
5.  26450  PhD Primož Lukšič  Computer intensive methods and applications  Researcher  2011 - 2014  96 
6.  02507  PhD Aleksander Malnič  Mathematics  Researcher  2011 - 2013  252 
7.  02887  PhD Dragan Marušič  Mathematics  Head  2011 - 2014  600 
8.  21656  PhD Štefko Miklavič  Mathematics  Researcher  2011 - 2014  201 
9.  30211  PhD Martin Milanič  Mathematics  Researcher  2011 - 2014  313 
10.  21658  PhD Alen Orbanić  Computer intensive methods and applications  Researcher  2011 - 2014  141 
11.  27777  PhD Enes Pasalic  Mathematics  Researcher  2011 - 2014  136 
12.  18838  PhD Primož Potočnik  Mathematics  Researcher  2011 - 2014  239 
13.  29820  PhD Dragan Stevanović  Mathematics  Researcher  2011 - 2014  135 
14.  23341  PhD Primož Šparl  Mathematics  Researcher  2011 - 2014  194 
15.  28229  PhD Aljaž Ule  Mathematics  Researcher  2011 - 2014  107 
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  10,877 
3.  2790  University of Primorska, Faculty of mathematics, Natural Sciences and Information Technologies  Koper  1810014009  17,881 
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 stands at the cutting edge of today’s research trends in AGT. It concentrates on some of the most relevant research areas within AGT. The current state of the art and important historical contributions are briefly sketched, and our main research goals, based on the past results and contributions of the project participants, are stated. These goals include the study of important open problems and conjectures in AGT, which presupposes a parallel in-depth investigation of various combinatorial objects together with development of the accompanying theoretical foundations, and last but not least, implementation of computational tools and algorithms. In spite of large potentials for concrete use of our results in certain branches of technology and industry, the focus of our research remains an overall development of mathematics as a universal language, and a permanent contribution to our civilisation. The project involves a number of researchers with excellent publishing records, currently active in Slovenia, guaranteeing research at the highest possible level. Nevertheless, a collaboration with three research institutions from Australia, Israel and USA where some of the most renowned world experts in AGT are based, is planned too. This will further enhance our research. The intensity of this collaboration together with their formal inclusion in the project depends on the financial situation (`bigger project’).
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. For example the outcome of our collaboration with `The Centre for the Mathematics of Symmetry and Computation' at the University of Western Australia, led by Cheryl Praeger, one of the leading world experts in AGT, represents a major contribution to the development of AGT.
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 is to increase innovation excellence in Europe in general, especially in member states underperforming in innovation. 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 2011, 2012, 2013, final report, complete report on dLib.si
Most important socioeconomically and culturally relevant results Annual report 2011, 2012, 2013, final report, complete report on dLib.si
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