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Non-identity order divisor graphs of groups | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 تیر 1404 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.28373.1716 | ||
| نویسندگان | ||
| M. Sattanathan1؛ J. Kottarathil* 2؛ I. Chakrabarty3 | ||
| 1Department of Mathematics, Sri Paramakalyani College, Alwarkurichi, Tenkasi- 627412Tamil Nadu | ||
| 2Department of Mathematics, St. Joseph's College, Moolamattom, India. | ||
| 3Department of Mathematics, CHRIST(Deemed to be University), Bangalore, 560029, Karnataka | ||
| چکیده | ||
| Let $G$ be a group with identity $e$. In this paper, we define and study the non-identity order divisor graph of $G$, where the vertex set is $G-\{e\}$ and two distinct vertices $x$ and $y$ are adjacent if and only if either $O(x)|O(y)$ or $O(y)|O(x)$. We denote the order divisor graph of group $G$ by $\o(G)$. We study some basic properties of $\o(G)$ such as connectedness, completeness, bipartiteness and Eulerian property. The lower bound as well as the number of edges of $\o(G)$ are also calculated for some group $G$ and some characterizations for fundamental properties of $\o(G)$ have been obtained. Finally, we explore the relation between the order prime graph and the non-identity order divisor graph of some group $G$. | ||
| کلیدواژه‌ها | ||
| Non-identity order divisor graph؛ order prime graph؛ Eulerian graph؛ finite group | ||
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آمار تعداد مشاهده مقاله: 5 |
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