P1-0285 — Annual report 2009
1.
Primitive bicirculant association schemes and a generalization of Wielandt's theorem

Bannai and Ito defined association scheme theory as doing ''group theory without groups'', thus raising a basic question as to which results about permutation groups are, in fact, results about association schemes? By considering transitive permutation groups in a wider setting of association schemes, it is shown that one such result is a generalisation from odd primes p to arbitrary prime powers pn, of the classical theorem of Wielandt about primitive permutation groups of degree 2p, p ) 2 a prime, being of rank 3.

COBISS.SI-ID: 1024198996
2.
Indirect punishment and generosity toward strangers

This article, published in the esteemed scientific journal Science, uses game theory and economic laboratory experiments with human subjects to study the impact of punishment on the evolution of co-operation between strangers. It is the first ever article in this journal by a researcher at a research institution in Slovenia that studies a social sciences topic.

COBISS.SI-ID: 1024190804
3.
A classification of cubic symmetric graphs of girth 6

In this article, published in a journal belonging to the first quarter of SCI journals in the field, a complete classification of cubic symmetric graphs of girth 6 is given. This classification is important in its self and also has an essential part in the proof of the existence of Hamilton cycle in cubic Cayley graphs arising from finite group having (2,s,3)-presentation for s divisible by 4. (H.H. Glover, K.Kutnar and D. Marušič, Hamiltonian cycles in cubic Cayley graphs: the (2,4k,3) case, J. Algebraic Combin. 30 (2009), 447-475.).

COBISS.SI-ID: 2724823
4.
Hamilton cycles in cubic Cayley graphs

This article, with an innovative approach for finding Hamilton paths/cycles in cubic Cayley graphs, based on embeddings onto appropriate closed orientable surfaces, gives constructions of Hamilton cycles in cubic Cayley graphs associated with groups having a (2,4k,3)-presentation. It thus gives an important step forward with respect to the long standing open problem of the existence of Hamilton cycles in connected Cayley graphs.

COBISS.SI-ID: 1024072020
5.
Probabilistic versus deterministic algebraic cryptanalysis

In this article, published in a top ranked journal, a theoretical analysis of the two branches of algebraic cryptanalysis is analyzed. It is shown that a deterministic algebraic cryptanalysis is a preferable cryptanalytic tool when compared to probabilistic cryptanalysis in terms of the attack complexity. This result answers some important open questions that have been raised in the literature.

COBISS.SI-ID: 1024137300