What question did this study set out to answer?

This research focuses on the properties of the comaximal ideal graph and its line graph associated with commutative rings.

June 14, 2026Open Access

SOME PROPERTIES OF SUPER-GRAPH OF (G (R) ) ᶜ AND ITS LINE GRAPH

KPKrishna PurohitRK University JPJaydeep ParejiyaGovernment Medical College

Key Points

This research focuses on the properties of the comaximal ideal graph and its line graph associated with commutative rings.
Defined the comaximal ideal graph G(R) based on the conditions of ideals in the ring R.
Examined adjacency conditions for vertices in G(R).
Analyzed properties and relationships within G(R) and its line graph.
Identified specific properties of G(R) concerning its vertex and edge structure.
Discussed implications of the adjacency conditions on the structure of the line graph.
Provided insights into the relationship between G(R) and the Jacobson radical of the ring.

Abstract

Let R be a commutative ring with identity 1≠0. The comaximal ideal graph of R is the simple, undirected graph whose vertex set is the set of all proper ideals of the ring R not contained in Jacobson radical of R and two vertices I and J are adjacent in this graph if and only if I+J=R. In this article, we have discussed the graph G(R) whose vertex set is the set of all proper ideals of ring R and two vertices I and J are adjacent in this graph if and only if I+J≠R. In this article, we have discussed some interesting results about G(R) and its line graph.

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