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A note on the extended total graph of commutative rings | ||
| Journal of Algebra and Related Topics | ||
| مقاله 2، دوره 6، شماره 1، شهریور 2018، صفحه 25-33 اصل مقاله (270.4 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2018.10241.1101 | ||
| نویسندگان | ||
| F. Esmaeili Khalil Saraei* 1؛ E. Navidinia2 | ||
| 1University of Tehran | ||
| 2Department of Mathematics, University of Guilan, Rasht, Iran | ||
| چکیده | ||
| Let $R$ be a commutative ring and $H$ a nonempty proper subset of $R$. In this paper, the extended total graph, denoted by $ET_{H}(R)$ is presented, where $H$ is a multiplicative-prime subset of $R$. It is the graph with all elements of $R$ as vertices, and for distinct $p,q\in R$, the vertices $p$ and $q$ are adjacent if and only if $rp+sq\in H$ for some $r,s\in R\setminus H$. We also study the two (induced) subgraphs $ET_{H}(H)$ and $ET_{H}(R\setminus H)$, with vertices $H$ and $R\setminus H$, respectively. Among other things, the diameter and the girth of $ET_{H}(R)$ are also studied. | ||
| کلیدواژه‌ها | ||
| Total graph؛ prime ideal؛ multiplicative-prime subset | ||
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آمار تعداد مشاهده مقاله: 853 تعداد دریافت فایل اصل مقاله: 971 |
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