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

Tetravalent vertex- and edge-transitive graphs over doubled cycles

In order to complete (and generalize) results of Gardiner and Praeger on 4-valent symmetric graphs (European J. Combin, 15 (1994)) we apply the method of lifting automorphisms in the context of elementary-abelian covering projections. In particular, the vertex- and edge-transitive graphs whose quotient by a normal $p$-elementary abelian group of automorphisms, for $p$ an odd prime, is a cycle, are described in terms of cyclic and negacyclic codes. Specifically, the symmetry properties of such graphs are derived from certain properties of the generating polynomials of cyclic and negacyclic codes, that is, from divisors of $x^n \pm 1 \in {\mathbb Z}_p[x]$. As an application, a short and unified description of resolved and unresolved cases of Gardiner and Praeger are given