The total graph of a commutative semiring with respect to proper ideals
عنوان مقاله: The total graph of a commutative semiring with respect to proper ideals
شناسه ملی مقاله: JR_JART-3-2_003
منتشر شده در در سال 1394
شناسه ملی مقاله: JR_JART-3-2_003
منتشر شده در در سال 1394
مشخصات نویسندگان مقاله:
Z. Ebrahimi Sarvandi - University of Guilan
S. Ebrahimi Atani - University of Guilan
خلاصه مقاله:
Z. Ebrahimi Sarvandi - University of Guilan
S. Ebrahimi Atani - University of Guilan
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.
کلمات کلیدی: Commutative semirings, Zero-divisor, Total graph
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/2026907/