6-Transitive graphs

Peter J. Cameron

doi:10.1016/0095-8956(80)90063-5

6-Transitive graphs

Peter J. Cameron^*

^*Corresponding author for this work

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

Abstract

A connected graph is n-transitive if, whenever two n-tuples are isometric, there is an automorphism mapping the first to the second. It is shown that a 6-transitive graph is complete multipartite, or complete bipartite with a matching deleted, or a cycle, or one of three special graphs on 9, 12 and 20 vertices. These graphs are n-transitive for all n; but there are graphs (the smallest on 56 vertices) which are 5- but not 6-transitive.

Original language	English
Pages (from-to)	168-179
Number of pages	12
Journal	Journal of Combinatorial Theory, Series B
Volume	28
Issue number	2
DOIs	https://doi.org/10.1016/0095-8956(80)90063-5
Publication status	Published - 1 Jan 1980

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title = "6-Transitive graphs",

abstract = "A connected graph is n-transitive if, whenever two n-tuples are isometric, there is an automorphism mapping the first to the second. It is shown that a 6-transitive graph is complete multipartite, or complete bipartite with a matching deleted, or a cycle, or one of three special graphs on 9, 12 and 20 vertices. These graphs are n-transitive for all n; but there are graphs (the smallest on 56 vertices) which are 5- but not 6-transitive.",

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N2 - A connected graph is n-transitive if, whenever two n-tuples are isometric, there is an automorphism mapping the first to the second. It is shown that a 6-transitive graph is complete multipartite, or complete bipartite with a matching deleted, or a cycle, or one of three special graphs on 9, 12 and 20 vertices. These graphs are n-transitive for all n; but there are graphs (the smallest on 56 vertices) which are 5- but not 6-transitive.

AB - A connected graph is n-transitive if, whenever two n-tuples are isometric, there is an automorphism mapping the first to the second. It is shown that a 6-transitive graph is complete multipartite, or complete bipartite with a matching deleted, or a cycle, or one of three special graphs on 9, 12 and 20 vertices. These graphs are n-transitive for all n; but there are graphs (the smallest on 56 vertices) which are 5- but not 6-transitive.

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U2 - 10.1016/0095-8956(80)90063-5

DO - 10.1016/0095-8956(80)90063-5

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AN - SCOPUS:0001127993

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EP - 179

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

IS - 2

ER -

6-Transitive graphs

Abstract

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