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Finite 2-Geodesic Transitive Abelian Cayley Graphs

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Abstract

In this paper, we first give a classification of the family of 2-geodesic transitive abelian Cayley graphs. Let \(\Gamma \) be such a graph which is not 2-arc transitive. It is shown that one of the following holds: (1) \(\Gamma \cong \mathrm{K}_{m[b]}\) for some \(m\ge 3\) and \(b\ge 2\); (2) \(\Gamma \) is a normal Cayley graph of an elementary abelian group; (3) \(\Gamma \) is a cover of Cayley graph \(\Gamma _K\) of an abelian group T / K, where either \(\Gamma _K\) is complete arc transitive or \(\Gamma _K\) is 2-geodesic transitive of girth 3, and A / K acts primitively on \(V(\Gamma _K)\) of type Affine or Product Action. Second, we completely determine the family of 2-geodesic transitive circulants.

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Acknowledgments

The authors are grateful to the anonymous referees for valuable suggestions and comments.

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Authors and Affiliations

  1. School of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, Jiangxi, People’s Republic of China

    Wei Jin

  2. Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, Jiangxi, People’s Republic of China

    Wei Jin

  3. School of Mathematics and Statistics, Central South University, Changsha, 410075, Hunan, People’s Republic of China

    Wei Jun Liu

  4. Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, Henan, People’s Republic of China

    Chang Qun Wang

Authors
  1. Wei Jin
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  2. Wei Jun Liu
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  3. Chang Qun Wang
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Correspondence to Wei Jin.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11271208, 11301230), NSF of Jiangxi (20142BAB211008, 20151BAB201001) and Jiangxi Education Department Grant (GJJ14351).

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Jin, W., Liu, W.J. & Wang, C.Q. Finite 2-Geodesic Transitive Abelian Cayley Graphs. Graphs and Combinatorics 32, 713–720 (2016). https://doi.org/10.1007/s00373-015-1601-y

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  • DOI: https://doi.org/10.1007/s00373-015-1601-y

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