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On the Classification of Arc-transitive Circulant Digraphs of Order Odd–Prime–Squared

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Abstract

A Cayley graph Γ = Cay(G, S) of a group G with respect to S is called a circulant digraph of order p k if G is a cyclic group of the same order. Investigated in this paper are the normality conditions for arc–transitive circulant (di)graphs of order p 2 and the classification of all such graphs. It is proved that any connected arc–transitive circulant digraph of order p 2 is, up to a graph isomorphism, either \( K_{{p^{2} }} \), G(p 2, r), or G(p, r)[pK 1], where r | p − 1.

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Authors and Affiliations

  1. LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

    Xue Wen Li

  2. Department of Mathematics, Tangshan Teacher’s College, Tangshan 063000, P. R. China

    Xue Wen Li

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  1. Xue Wen Li
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Correspondence to Xue Wen Li.

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Research supported by the National Natural Science Foundation of China under Grant No. 103710003

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Li, X.W. On the Classification of Arc-transitive Circulant Digraphs of Order Odd–Prime–Squared. Acta Math Sinica 21, 1131–1136 (2005). https://doi.org/10.1007/s10114-005-0577-6

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  • DOI: https://doi.org/10.1007/s10114-005-0577-6

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