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Commutators-based graph in polygroup | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 4 - شماره پیاپی 29، اسفند 2024، صفحه 39-52 اصل مقاله (523.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.22105.1501 | ||
| نویسندگان | ||
| Mohammad Hamidi* ؛ Elahe Mohammadzadeh؛ Somayeh Amirmofidi | ||
| Department of Mathematics, University of Payame Noor, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Polygroup؛ Related graph؛ Commutator | ||
| مراجع | ||
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