Remarks on path-transitivity in finite graphs

Abstract

This paper deals with graphs the automorphism groups of which are transitive on vertices and on undirected paths (but not necessarily on directed walks) of some fixed length. In particular, it is shown that if the automorphism group G of a graph Γ is transitive on vertices and on undirected paths of length k + 1 in Γ, for some k ≥ 1, then G is also transitive on k-arcs in Γ. Further details are given for the case k = 1, for the case of cubic graphs, and for the case k > 4. © 1996 Academic Press Limited.