s-Route

An -route of a graph  is a sequence of vertices  of  such that  for , 1, ...,  (where  is the edge set of ) and  for , 2, ..., .

If a graph  contains an -route with , then  is said to be -transitive, -arc-transitive, or arc-transitive of order  if the automorphism group of  acts transitively on all -routes.

Note that some authors present other letters to , for example  (Harary 1994) and .

REFERENCES

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 200, 1994.

Holton, D. A. and Sheehan, J. The Petersen Graph. Cambridge, England: Cambridge University Press, pp. 202-210, 1993.