04093489

j

04093489 Seifter, Norbert Properties of graphs with polynomial growth. J. Comb. Theory, Ser. B 52, No.2, 222-235 (1991). 1991 Elsevier Science (Academic Press), San Diego, CA EN connected locally finite transitive growth automorphism group

doi:10.1016/0095-8956(91)90064-Q

Let X be a connected locally finite transitive growth. We prove that groups with intermediate growth cannot act transitively on X. Furthermore it follows from this result that the automorphism group AUT(X) is uncountable if and only if it contains a finitely generated subgroup with exponential growth which acts transitively on X. If X has valency at least three, we prove that X cannot be 8-transitive. N.Seifter