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Generalized order divisor graphs of finite group | ||
| International Journal of Group Theory | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 15 آبان 1401 اصل مقاله (846.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2022.133091.1787 | ||
| نویسندگان | ||
| Parinyawat Choosuwan1؛ Pannarin Sangsawang2؛ Cheevarat Matwangsang2؛ Sireethon Thongsupol2؛ Siripong Sirisuk* 2 | ||
| 1Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Tech- nology Thanyaburi (RMUTT), 12110, Pathum Thani, Thailand | ||
| 2Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, 12120, Pathum Thani, Thailand | ||
| چکیده | ||
| Let $G$ be a finite group and $k$ a fixed positive integer. We define the generalized order divisor graph of $G$ to be a graph whose vertex set is the group $G$ and in which two vertices $a$ and $b$ are adjacent if and only if the orders $o(a^k)$ and $o(b^k)$ are different and either $o(a^k)$ divides $o(b^k)$ or $o(b^k)$ divides $o(a^k)$. This generalizes the order divisor graphs of finite groups. Some properties of our graph are introduced, and we investigate the structure of the generalized order divisor graphs of finite cyclic groups. | ||
| کلیدواژه‌ها | ||
| Power graph؛ star graph؛ cyclic group | ||
| مراجع | ||
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