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Some results on a supergraph of the comaximal ideal graph of a commutative ring | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 3، شماره 2، اسفند 2018، صفحه 151-172 اصل مقاله (454.27 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2018.26132.1079 | ||
| نویسندگان | ||
| S. Visweswaran* 1؛ Jaydeep Parejiya2 | ||
| 1Saurashtra University | ||
| 2Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India. | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity such that $R$ admits at least two maximal ideals. In this article, we associate a graph with $R$ whose vertex set is the set of all proper ideals $I$ of $R$ such that $I$ is not contained in the Jacobson radical of $R$ and distinct vertices $I$ and $J$ are joined by an edge if and only if $I$ and $J$ are not comparable under the inclusion relation. The aim of this article is to study the interplay between the graph-theoretic properties of this graph and the ring-theoretic properties of the ring $R$. | ||
| کلیدواژه‌ها | ||
| Chained ring؛ Bipartite graph؛ Split graph؛ Complemented graph | ||
| مراجع | ||
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