Cayley Graphs Over Green \(^*\) Relations of Abundant Semigroups
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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.
KeywordsAbundant semigroups Cayley graphs over Green \(^*\) relations Transmissible Linear graphs Complete graphs
Mathematics Subject Classification06F05 20M10
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).
- 14.Navges, H., Amir, A.: Graph operations on Cayley graphs of semigroups. Int. J. Appl. Math. Res. 3, 54–57 (2014)Google Scholar