In this book a formal model of social dilemma with partner selection is introduced and studied with the methods of standard game theory, laboratory experiments and computer simulations. It allows exploration of simultaneous dynamics of the network structure and cooperative behavior on this structure. The results show that free partner choice strongly facilitates cooperation and leads to networks where free-riders are likely to be excluded.

COBISS.SI-ID: 14604377

It is shown that a vertex-transitive graph of valency p+1, p a prime, admitting a transitive action of a {2,p}-group, has a non-identity semiregular automorphism. As a consequence, it is proved that a quartic vertex-transitive graph has a non-identity semiregular automorphism, thus giving a partial affirmative answer to the conjecture that all vertex-transitive graphs have such an automorphism and, more generally, that all 2-closed transitive permutation groups contain such an element (see [Discrete Math. 36 (1981) 69–81; Discrete Math. 167/168 (1997) 605–615]).

COBISS.SI-ID: 14287961

This article, published in the journal that ranks in the top 10% SCI mathematical journals over the last few years, gives an innovative approach to finding Hamilton paths/cycles in cubic Cayley graphs, a problem that has been open for 40 years. The method is based on graph embeddings onto appropriate closed orientable surfaces and leads to constructions of Hamilton paths in cubic Cayley graphs associated with groups having a (2,s,3)-presentation.

COBISS.SI-ID: 14418521

In this article it is shown that every distance-regular graph of negative type (DRNT) which is almost-polygon is also 1-homogeneous. And, for a DRNT which is not almost-polygons it is shown that it possesses a certain, from the starting vertex independent, equitable partition of its vertex set which involves 4d-1 cells. Since DRNT have many properties we can control them in a greater deal as distance-regular graphs in general. Consequently, their complete classification might be given in the near future. The results of this article will essentially contribute to this classification.

COBISS.SI-ID: 13783129

In this article a complete classification of 2-arc-transitive Cayley graphs of dihedral groups is given. An essential role in obtaining this deep result is the thorough analysis of 2-arc-transitive Cayley graphs of dihedral groups given in [D.Marušič, On 2-arc-transitivity of Cayley graphs, J. Combin. Theory B, 87 (2003), 162—196] combined together with the covering graph techniques.

COBISS.SI-ID: 2018277