Basic Research Project J1-6720
Algebraic Graph Theory with Applications

 

Project Title: Algebraic Graph Theory with Applications.

PI: Dragan Marušič.

Project Code: J1-6720.

Type of the Project: basic research project.

Funding Organization: Slovenian Research Agency (ARRS).

Research Field (ARRS): 1.01.00 - Natural Sciences and Mathematics / Mathematics.

Duration: 1. 7. 2014 - 30. 6. 2017.

Project Category: B.

Yearly Range: 0,94 FTE (1596 research hours).

Sicris profile of the project is avaliable here.

Research Organizations:
University of Primorska, Andrej Marušič Institute,
University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies,
University of Ljubljana, Faculty of Education.

Project Members:

Berčič Katja (ARRS code: 33231) Cerinšek Monika (ARRS code: 33987) Dobson Edward Tauscher (ARRS code: 34109) Kaliada Olga (TEH) (ARRS code: 35727) Košmrlj Gašper (ARRS code: 34750) Kovacs Istvan (ARRS code: 25997) Kovač Boštjan (ARRS code: 34751) Kutnar Klavdija (ARRS code: 24997) Kuzman Boštjan (ARRS code: 23501) Malnič Aleksander (ARRS code: 02507) Marušič Dragan (PI) (ARRS code: 02887) Miklavič Štefko (ARRS code: 21656) Milanič Martin (ARRS code: 30211) Pasalic Enes (ARRS code: 27777) Pisanski Tomaž (ARRS code: 01941) Potočnik Primož (ARRS code: 18838) Stevanović Dragan (ARRS code: 29820) Šparl Primož (ARRS code: 23341) Verret Gabriel (ARRS code: 28586)

 

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 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.