## Remarks on path-transitivity in finite graphs.(English)Zbl 0871.05029

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 $$\operatorname{Aut}(G)$$ is transitive on vertices and on paths of length $$k+1$$, then $$\operatorname{Aut} (G)$$ is also transitive on $$k$$-arcs. The paper contains some interesting examples and more details for the case of cubic graphs.

### MSC:

 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C38 Paths and cycles
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