TY - JOUR ID - 13778 TI - Some results on a supergraph of the comaximal ideal graph of a commutative ring JO - Communications in Combinatorics and Optimization JA - CCO LA - en SN - 2538-2128 AU - Visweswaran, S. AU - Parejiya, Jaydeep AD - Saurashtra University AD - Department of Mathematics, Saurashtra University, Rajkot, Gujarat, India. Y1 - 2018 PY - 2018 VL - 3 IS - 2 SP - 151 EP - 172 KW - Chained ring KW - Bipartite graph KW - Split graph KW - Complemented graph DO - 10.22049/cco.2018.26132.1079 N2 - 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 $R$. UR - http://comb-opt.azaruniv.ac.ir/article_13778.html L1 - http://comb-opt.azaruniv.ac.ir/article_13778_c5b20d65e49415f10224ec5da091faf6.pdf ER -