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Graphs and Combinatorics

, Volume 35, Issue 6, pp 1609–1617 | Cite as

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

  • Chunhua LiEmail author
  • Baogen Xu
  • Huawei Huang
Original Paper

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.

Keywords

Abundant semigroups Cayley graphs over Green \(^*\) relations Transmissible Linear graphs Complete graphs 

Mathematics Subject Classification

06F05 20M10 

Notes

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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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of ScienceEast China Jiaotong UniversityNanchangChina
  2. 2.School of Mathematics and Computer ScienceGuizhou Normal UniversityGuiyangChina

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