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 -