پیوندهای مفید
آمار
| تعداد نشریات | 7 |
| تعداد شماره‌ها | 399 |
| تعداد مقالات | 5,389 |
| تعداد مشاهده مقاله | 5,288,012 |
| تعداد دریافت فایل اصل مقاله | 4,882,748 |
Perfectness of the essential graph for modules over commutative rings | ||
| AUT Journal of Mathematics and Computing | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 دی 1402 | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22138.1136 | ||
| نویسندگان | ||
| Shiroyeh Payrovi* ؛ Fatemeh Soheilnia؛ Ali Behtoei | ||
| Department of Pure Mathematics, Faculty of Science, Imam Khomieini International University, Postal Code: 34149-1-6818, Qazvin, Iran | ||
| چکیده | ||
| Let $R$ be a commutative ring and $M$ be an $R$-module. The essential graph of $M$, denoted by $EG(M)$ is a simple graph with vertex set $Z(M) \setminus {\rm{Ann}}_R(M)$ and two distinct vertices $x,y \in Z(M) \setminus {\rm{Ann}}_R(M)$ are adjacent if and only if ${\rm{Ann}}_M(xy)$ is an essential submodule of $M$. In this paper, we investigate the dominating set, the clique and the chromatic numbers and the metric dimension of the essential graph for Noetherian modules. Let $M$ be a Noetherian $R$-module such that $\mid {\rm MinAss}_R(M)\mid=n\geq 2$ and let $EG(M)$ be a connected graph. We prove that $EG(M)$ is weakly prefect, that is, $\omega(EG(M))=\chi(EG(M))$. Furthermore, it is shown that ${\rm dim}(EG(M))=\mid Z(M)\mid-(\mid {\rm{Ann}}(M)\mid+2^n)$, whenever $r({\rm{Ann}}(M) )\neq{\rm{Ann}}(M)$ and ${\rm dim}(EG(M))=\mid Z(M)\mid-(\mid {\rm{Ann}}(M)\mid+2^n-2)$, whenever $r({\rm{Ann}}(M) )= {\rm{Ann}}(M)$. | ||
| کلیدواژه‌ها | ||
| Essential graph؛ Dominating set؛ Clique number؛ Chromatic number؛ Metric dimension | ||
|
آمار تعداد مشاهده مقاله: 472 |
||