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Projects / Programmes source: ARIS

Algebraic methods in graph theory and finite geometries

Periods
Research activity

Code Science Field Subfield
1.01.00  Natural sciences and mathematics  Mathematics   

Code Science Field
P110  Natural sciences and mathematics  Mathematical logic, set theory, combinatories 
P120  Natural sciences and mathematics  Number theory, field theory, algebraic geometry, algebra, group theory 
P150  Natural sciences and mathematics  Geometry, algebraic topology 
Evaluation (rules)
source: COBISS
Researchers (6)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  00755  MSc Marko Lovrečič Saražin  Mathematics  Researcher  2001 - 2003  30 
2.  02507  PhD Aleksander Malnič  Mathematics  Researcher  2001 - 2003  250 
3.  02887  PhD Dragan Marušič  Mathematics  Head  2001 - 2003  598 
4.  18838  PhD Primož Potočnik  Mathematics  Researcher  2001 - 2003  238 
5.  03231  PhD Marko Razpet  Mathematics  Researcher  2001 - 2003  783 
6.  11687  PhD Boris Zgrablić  Mathematics  Researcher  2001 - 2003  56 
Organisations (1)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  19,647 
Abstract
The program involves a happy interplay of three areas of mathematics: first, group actions on combinatorial objects (semiregular elements of permutation groups, lifts of automorphisms, various transitivity conditions on graphs), second, a study of purely graph-theoretic concepts (distance -transitivity, hamiltonicity), and third, structural properties of certain objects in finite geometries. Much of this program will be devoted to half-arc-transitive group actions on graphs, in particular, graphs of valency 4. Our main interest lies in the study of structural properties and classification problems for such graphs. Getting an understanding of the structure of the corresponding vertex stabilizers will be one of our goals in that respect. Furthermore, 2-arc-transitive Cayley graphs of abelian and dihedral groups will also be dealt with. The open problem of existence of semiregular elements in 2-closed transitive permutation groups will also be touched upon. Last but not least, distance-regular graphs, hamiltonian properties of graphs and arcs in projective planes are also going to be considered. A monograph on transiitve group actions on graphs is a long-term goal of the research group involved in this program.
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