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A Classification of Spectrum-determined Circulant Digraphs

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A Correction to this article was published on 08 October 2021

Abstract

Some researchers have proved that ádám’s conjecture is wrong. However, under special conditions, it is right. Let Zn be a cyclic group of order n and Cn(S) be the circulant digraph of Zn with respect to S ⊆ Zn\{0}. In the literature, some people have used a spectral method to solve the isomorphism for the circulants of prime-power order. In this paper, we also use the spectral method to characterize the circulants of order paqbwc(where p, q and w are all distinct primes), and to make ádám’s conjecture right.

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Authors and Affiliations

  1. School of Mathematics and Information Technology, Jiangsu Second Normal University, Nanjing, 210013, China

    Zheng-xin Qin

  2. Department of Mathematics, Xinjiang University, Urumuqi, 830054, China

    Ji-xiang Meng & Qiong-xiang Huang

Authors
  1. Zheng-xin Qin
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  2. Ji-xiang Meng
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  3. Qiong-xiang Huang
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Corresponding author

Correspondence to Ji-xiang Meng.

Additional information

The research is supported by Start high-level personnel of scientific research funds of Jiangsu Second Normal University (No. 918001) and NSFC(11171283).

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Qin, Zx., Meng, Jx. & Huang, Qx. A Classification of Spectrum-determined Circulant Digraphs. Acta Math. Appl. Sin. Engl. Ser. 34, 703–709 (2018). https://doi.org/10.1007/s10255-018-0778-0

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  • DOI: https://doi.org/10.1007/s10255-018-0778-0

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