Properties of graphs with polynomial growth

Norbert Seifter

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

Properties of graphs with polynomial growth

Norbert Seifter

Chair of Applied Mathematics (170)

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

Abstract

Let X be a connected locally finite transitive graph with polynomial 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.

Original language	English
Pages (from-to)	222-235
Number of pages	14
Journal	Journal of combinatorial theory. Series B
Volume	52.1991
Issue number	2
DOIs	https://doi.org/10.1016/0095-8956(91)90064-Q
Publication status	Published - 1991

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title = "Properties of graphs with polynomial growth",

abstract = "Let X be a connected locally finite transitive graph with polynomial 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.",

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AB - Let X be a connected locally finite transitive graph with polynomial 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.

UR - https://doi.org/10.1016/0095-8956(91)90064-Q

U2 - 10.1016/0095-8956(91)90064-Q

DO - 10.1016/0095-8956(91)90064-Q

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VL - 52.1991

SP - 222

EP - 235

JO - Journal of combinatorial theory. Series B

JF - Journal of combinatorial theory. Series B

IS - 2

ER -

Properties of graphs with polynomial growth

Abstract

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