Some results on a supergraph of the comaximal ideal graph of a commutative ring

Visweswaran, S.; Parejiya, Jaydeep

doi:10.22049/cco.2018.26132.1079

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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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Some results on a supergraph of the comaximal ideal graph of a commutative ring