Dva-ločno-tranzitivni dvo-valentni digrafi določenih redov

The topic of this paper is digraphs of in-valence and out-valence 2 that admit a 2-arc-transitive group of automorphisms. We classify such digraphs that satisfy certain additional conditions on their order. In particular, a classification of those with order ▫$kp$▫ or ▫$kp^{2}$▫ where ▫$k leq 14$▫ and ▫$p$▫ is a prime can be deduced from the results of this paper.Tema tega članka so digrafi vhodne in izhodne valence 2, ki dopuščajo 2-ločno-tranzitivno grupo avtomorfizmov. Klasificiramo takšne digrafe, ki zadoščajo določenim dodatnim pogojem glede njihovega reda. Tako je npr. mogoče s pomočjo rezultatov tega članka klasificirati tiste, ki imajo red ▫$kp$▫ ali ▫$kp^{2}$▫, kjer je ▫$k leq 14$▫ in je ▫$p$▫ praštevilo

On the Automorphism Groups of Almost All Circulant Graphs and Digraphs

We attempt to determine the structure of the automorphism group of a generic circulant graph. We first show that almost all circulant graphs have automorphism groups as small as possible. Dobson has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism groups are not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose orders are in a “large” subset of integers. We note that all non-normal circulant (di)graphs can be classified into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph