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Planarity of the essential graph for modules | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 بهمن 1404 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.30608.1799 | ||
| نویسندگان | ||
| S. Azlesh؛ Sh. Payrovi* ؛ F. Soheilnia | ||
| Department of Mathematics, Imam Khomeini International University, Qazvin, Iran | ||
| چکیده | ||
| Given a module $\mathcal{M}$ over a commutative ring $\mathcal{R}$, we can construct a simple graph $EG\mathcal{(M)}$ with the vertex set $\mathcal{Z_R(M)} \setminus \mathcal{{\rm Ann}_R(M)}$. Two distinct vertices $x, y$ are connected whenever ${\rm Ann}_{\mathcal{M}}(xy)$ is an essential submodule of $\mathcal{M}$. The present study provides a detailed analysis of planar zero-divisor and planar essential graphs, especially when they possess a universal vertex. It demonstrates that such graphs can be represented as join of some known graphs. Additionally, it examines that whether the zero-divisor and the essential graphs of $\mathbb{Z}_n$ are planar or not. | ||
| کلیدواژهها | ||
| Zero-divisor graph؛ Essential graph؛ Planar graph | ||
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آمار تعداد مشاهده مقاله: 24 |
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