Commutators-based graph in polygroup

Author(s):

Mohammad Hamidi * , Elahe Mohammadzadeh , Somayeh Amirmofidi

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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.

Keywords:

Polygroup‎ , ‎Related Graph‎ , ‎Commutator

Language:
English
Published:
Journal of Mahani Mathematical Research, Volume:13 Issue: 2, Summer and Autumn 2024
Pages:
39 to 52
https://www.magiran.com/p2797831