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Cayley Graphs Over Green \(^*\) Relations of Abundant Semigroups

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Abstract

In this paper, we first introduce the concept of Cayley graphs over Green \(^*\) relations of abundant semigroups by using Green \(^*\) relations. After obtaining some basic properties, we get some conditions for Cayley graphs over Green \(^*\) relations of abundant semigroups to be transmissible. Finally, we give necessary and sufficient conditions for a Cayley graph over Green \(^*\) relations of an abundant semigroup to be linear and complete, respectively.

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Acknowledgements

The authors are very grateful to the referees for their valuable suggestions which lead to an improvement of this paper.

This work is supported by the National Science Foundation of China (Nos. 11261018, 11961026), the Natural Science Foundation of Jiangxi Province (Nos. 20181BAB201002, 20171BAB201009).

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Authors and Affiliations

  1. School of Science, East China Jiaotong University, Nanchang, 330013, Jiangxi, China

    Chunhua Li & Baogen Xu

  2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, Guizhou, China

    Huawei Huang

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  1. Chunhua Li
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  2. Baogen Xu
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  3. Huawei Huang
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Correspondence to Chunhua Li.

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Li, C., Xu, B. & Huang, H. Cayley Graphs Over Green \(^*\) Relations of Abundant Semigroups. Graphs and Combinatorics 35, 1609–1617 (2019). https://doi.org/10.1007/s00373-019-02106-2

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  • DOI: https://doi.org/10.1007/s00373-019-02106-2

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