There exists no tetravalent half-arc-transitive graph of order 2p2

AbstractA graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not arc set. In this paper, we show that there is no tetravalent half-arc-transitive graph of order 2p2

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