Abstract: A complete list of all connected arc-transitive asymmetric digraphs of in-valence and out-valence 2 on up to 1000 vertices is presented. As a byproduct, a complete list of all connected 4-valent graphs admitting a half-arc-transitive group of automorphisms on up to 1000 vertices is obtained. Several graph-theoretical properties of the elements of our census are calculated and discussed.Keywords: graphs, digraphs, edge-transitive, vertex-transitive, arc-transitive, half arc-transitivePublished in RUP: 31.12.2021; Views: 2222; Downloads: 19 Full text (370,47 KB)
Keywords: deleted wreath product of digraphs, automorphism group, half-arc-transitivePublished in RUP: 14.11.2019; Views: 3174; Downloads: 99 Link to full text
Abstract: Given integers ▫$k$▫ and ▫$m$▫, we construct a ▫$G$▫-arc-transitive graph of valency ▫$k$▫ and an ▫$L$▫-arc-transitive oriented digraph of out-valency ▫$k$▫ such that ▫$G$▫ and ▫$L$▫ both admit blocks of imprimitivity of size ▫$m$▫.Keywords: arc-transitive digraphs, Cayley digraphs, imprimitive digraphsPublished in RUP: 28.06.2019; Views: 2862; Downloads: 130 Link to full text
