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The co-prime power order graph of a finite group | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 1، مهر 2025، صفحه 45-52 اصل مقاله (156.3 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.24886.1547 | ||
| نویسندگان | ||
| H. H. Mushatet1؛ A. A. Talebi* 2 | ||
| 1Ministry of Education, Dhi Qar Education Directorate, Iraq | ||
| 2Department of Mathematics, University of Mazandaran, Babolsar, Iran | ||
| چکیده | ||
| In this study, we generalized the co-prime graph of a finite group called the co-prime power order graph of a finite group. It is denoted by $\beta_G$, and its vertex set is $G$, such that two distinct vertices $x$ and $y$ are adjacent if and only if $\operatorname{gcd}(|x|,|y|)=p^n$, where $p$ is a prime number, and $n \in \mathbb{Z}^{+} \cup\{0\}$. We characterized complete graphs and planar graphs on the co-prime power order graphs, and investigated some properties of graph $\beta_G$ for some groups such as cyclic groups, dihedral groups, and the generalized quaternion groups, and obtained the vertex-connectivity among them. Finally, we characterized some induced subgraphs of co-prime power order graph for some finite groups. | ||
| کلیدواژه‌ها | ||
| Cyclic group؛ Dihedral group؛ Generalized quaternion group؛ Complete graph؛ Planar graph؛ Co-prime order graph؛ Induced graph؛ Vertex-connectivity | ||
| مراجع | ||
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