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A Note on a graph associated to a commutative ring | ||
| Journal of Algebra and Related Topics | ||
| مقاله 6، دوره 5، شماره 1، شهریور 2017، صفحه 61-82 اصل مقاله (357.96 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2017.2399 | ||
| نویسندگان | ||
| S. Visweswaran* ؛ J. Parejiya | ||
| Saurashtra University | ||
| چکیده | ||
| The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings. In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rx\cap Ry = Rxy$. In Section 2 of this article, we classify rings $R$ such that $G(R)$ is complete and we also consider the problem of determining rings $R$ such that $\chi(G(R)) = \omega(G(R))< \infty$. In Section 3 of this article, we classify rings $R$ such that $G(R)$ is planar. | ||
| کلیدواژه‌ها | ||
| Comaximal graph of a ring؛ complete graph؛ chromatic number؛ clique number؛ planar graph | ||
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