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The total graph of a commutative semiring with respect to proper ideals | ||
| Journal of Algebra and Related Topics | ||
| مقاله 3، دوره 3، شماره 2، اسفند 2015، صفحه 27-41 اصل مقاله (288.02 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Z. Ebrahimi Sarvandi* ؛ S. Ebrahimi Atani | ||
| University of Guilan | ||
| چکیده | ||
| Let $I$ be a proper ideal of a commutative semiring $R$ and let $P(I)$ be the set of all elements of $R$ that are not prime to $I$. In this paper, we investigate the total graph of $R$ with respect to $I$, denoted by $T(\Gamma_{I} (R))$. It is the (undirected) graph with elements of $R$ as vertices, and for distinct $x, y \in R$, the vertices $x$ and $y$ are adjacent if and only if $x + y \in P(I)$. The properties and possible structures of the two (induced) subgraphs $P(\Gamma_{I} (R))$ and $\bar {P}(\Gamma_{I} (R))$ of $T(\Gamma_{I} (R))$, with vertices $P(I)$ and $R - P(I)$, respectively are studied. | ||
| کلیدواژهها | ||
| Commutative semirings؛ Zero-divisor؛ Total graph | ||
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آمار تعداد مشاهده مقاله: 1,820 تعداد دریافت فایل اصل مقاله: 1,694 |
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