Arc-transitive graph

Arc-transitive graph

In mathematics, an arc-transitive graph is a graph "G" such that, given any two edges "e"1 = "u"1"v"1 and "e"2 = "u"2"v"2 of "G", there are two automorphisms

:"f" : "G" → "G", "g" : "G" → "G"

such that

:"f" (e1) = e2, "g" (e1) = e2

and

:"f" ("u"1) = "u"2, "f" ("v"1) = "v"2, :"g" ("u"1) = "v"2, "g" ("v"1) = "u"2.

In other words, a graph is arc-transitive if its automorphism group acts transitively upon its arcs.


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