Basic Research Project J1-5433
Application of Semiregular Group Actions in some Open Problems in Algebraic Graph Theory

 

Project Title: Application of Semiregular Group Actions in some Open Problems in Algebraic Graph Theory.

PI: Dragan Marušič.

Project Code: J1-5433.

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. 8. 2013 - 31. 7. 2016.

Project Category: B.

Yearly Range: 0,94 FTE (1603 research hours).

Sicris profile of the project is avaliable here.

Research Organizations:
University of Primorska, Andrej Marušič Institute,
University of Ljubljana, Faculty of Education.

Project Members:

Banič Iztok (ARRS code: 23201)

Batagelj Vladimir (ARRS code: 01467)

Kovacs Istvan (ARRS code: 25997)

Kuzman Boštjan (ARRS code: 23501)

Malnič Aleksander (ARRS code: 02507)

Marušič Dragan (ARRS code: 02887)

Miklavič Štefko (ARRS code: 21656)

Milanič Martin (ARRS code: 30211)

Potočnik Primož (ARRS code: 18838)

Stevanović Dragan (ARRS code: 29820)

Strašek Rok (ARRS code: 17808)

Šparl Petra (ARRS code: 20495)

Šparl Primož (ARRS code: 23341)

Taranenko Andrej (ARRS code: 21821)

Tisnikar Viljem (ARRS code: 34799)

 

Abstract:

This project 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).

The motivation comes from an open problem, posed in 1981, when the project 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 project will involve work on various aspects of this problem, with applications to other open problems in algebraic graph theory.