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

Document Type : Original Manuscript

Authors

1 Department of Applied Sciences, RK University, P.O. Box 360003, Rajkot, India.

2 Department of Mathematics, Government Polytechnic, P.O. Box 360003, Rajkot, India.

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.

Keywords

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