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Date: 6-3-2022
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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 .
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.
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