Local 2-Geodesic Transitivity of Graphs

Alice Devillers; W. Jin; Cai-Heng Li; A. Seress

doi:10.1007/s00026-014-0224-y

Local 2-Geodesic Transitivity of Graphs

Alice Devillers, W. Jin, Cai-Heng Li, A. Seress

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

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Abstract

An s-geodesic in a graph Γ is a path connecting two vertices at distance s. Being locally transitive on s-geodesics is not a monotone property: if an automorphism group G of a graph Γ is locally transitive on s-geodesics, it does not follow that G is locally transitive on shorter geodesics. In this paper, we characterise all graphs that are locally transitive on 2-geodesics, but not locally transitive on 1-geodesics. © 2014 Springer Basel.

Original language	English
Pages (from-to)	313-325
Number of pages	13
Journal	Annals of Combinatorics
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s00026-014-0224-y
Publication status	Published - 2014

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title = "Local 2-Geodesic Transitivity of Graphs",

abstract = "An s-geodesic in a graph Γ is a path connecting two vertices at distance s. Being locally transitive on s-geodesics is not a monotone property: if an automorphism group G of a graph Γ is locally transitive on s-geodesics, it does not follow that G is locally transitive on shorter geodesics. In this paper, we characterise all graphs that are locally transitive on 2-geodesics, but not locally transitive on 1-geodesics. {\textcopyright} 2014 Springer Basel.",

author = "Alice Devillers and W. Jin and Cai-Heng Li and A. Seress",

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doi = "10.1007/s00026-014-0224-y",

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AU - Devillers, Alice

AU - Jin, W.

AU - Li, Cai-Heng

AU - Seress, A.

PY - 2014

Y1 - 2014

N2 - An s-geodesic in a graph Γ is a path connecting two vertices at distance s. Being locally transitive on s-geodesics is not a monotone property: if an automorphism group G of a graph Γ is locally transitive on s-geodesics, it does not follow that G is locally transitive on shorter geodesics. In this paper, we characterise all graphs that are locally transitive on 2-geodesics, but not locally transitive on 1-geodesics. © 2014 Springer Basel.

AB - An s-geodesic in a graph Γ is a path connecting two vertices at distance s. Being locally transitive on s-geodesics is not a monotone property: if an automorphism group G of a graph Γ is locally transitive on s-geodesics, it does not follow that G is locally transitive on shorter geodesics. In this paper, we characterise all graphs that are locally transitive on 2-geodesics, but not locally transitive on 1-geodesics. © 2014 Springer Basel.

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DO - 10.1007/s00026-014-0224-y

M3 - Article

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VL - 18

SP - 313

EP - 325

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 2

ER -

Local 2-Geodesic Transitivity of Graphs

Abstract

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