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Local 2-Geodesic Transitivity of Graphs

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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.

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References

  1. Devillers A., Jin W., Li C.H., Praeger C.E.: Local 2-geodesic transitivity and clique graphs. J. Combin. Theory Ser. A 120(2), 500–508 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  2. Devillers A., Jin W., Li C.H., Praeger C.E.: Line graphs and geodesic transitivity. Ars Math. Contemp. 6, 13–20 (2013)

    MathSciNet  Google Scholar 

  3. Fang X.G., Li C.H., Praeger C.E.: The locally 2-arc transitive graphs admitting a Ree simple group. J. Algebra 282(2), 638–666 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Giudici M., Li C.H., Praeger C.E.: Analysing finite locally s-arc transitive graphs. Trans. Amer. Math. Soc. 356(1), 291–317 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Leemans D.: Locally s-arc-transitive graphs related to sporadic simple groups. J. Algebra 322(3), 882–892 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Weiss R.: Groups with a (B, N)-pair and locally transitive graphs. Nagoya Math. J. 74, 1–21 (1979)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Western Australia, Crawley, WA, 6009, Australia

    Alice Devillers & Cai Heng Li

  2. School of Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, 330013, P.R. China

    Wei Jin

  3. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Ákos Seress

Authors
  1. Alice Devillers
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  2. Wei Jin
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  3. Cai Heng Li
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  4. Ákos Seress
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Corresponding author

Correspondence to Alice Devillers.

Additional information

Dedicated to the memory of our colleague Ákos, who passed away too soon.

Alice, Cai Heng, and Wei

C. H. Li and Á . Seress were partially supported by DP1096525 of the Australian Research Council. Seress was also partially supported by the NSF. W. Jin was supported by a SIRF Scholarship at UWA and is now supported by the NNSF of China (11301230).

Ákos Seress is deceased (1958–2013).

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Devillers, A., Jin, W., Li, C.H. et al. Local 2-Geodesic Transitivity of Graphs. Ann. Comb. 18, 313–325 (2014). https://doi.org/10.1007/s00026-014-0224-y

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  • DOI: https://doi.org/10.1007/s00026-014-0224-y

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