Commutators-based graph in polygroup

Document Type : Research Paper

Authors

Department of Mathematics, University of Payame Noor, Tehran, Iran

Abstract

In this paper, first, we study commutators of a polygroup. Then for a finite polygroup $P$ and a fixed element $g \in P$, we introduce the $g$-graph $\Delta_P^g$. In addition, with some additional conditions, we see that it is connected and the diameter is at most $3$. Then, we investigate isomorphic graphs. Specially, we obtain a new isomorphic graph derived from an isomorphic graph and two non-commutative isomorphic polygroups. Also, we show that two polygroups with  isomorphic graphs preserve nilpotency.

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References

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Journal of Mahani Mathematical Research
Volume 13, Issue 4 - Serial Number 29
Special issue dedicated to Professor Esfandiar Eslami
December 2024
Pages 39-52

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History

  • Receive Date: 28 August 2023
  • Revise Date: 27 November 2023
  • Accept Date: 18 January 2024

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