Remarks on path-transitivity in finite graphs
The paper deals with graphs whose automorphism groups act transitively on vertices and on undirected paths of certain fixed length. The authors show that if for a graph \(G\) its automorphism group \(\Aut(G)\) is transitive on vertices and on paths of length \(k+1\), then \(\Aut (G)\) is also transitive on \(k\)-arcs. The paper contains some interesting examples and more details for the case of cubic graphs.
scientific article; zbMATH DE number 895873