Thickness of line graph of intersection graph of ideals of rings

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Abstract
Let [ ] be a commutative ring with unity and [ ] be the set of all nontrivial proper ideals of [ ]. The intersection graph of ideals of a ring [ ], denoted by [ ], is an undirected simple graph (no loops and no parallel edges) with vertex set [ ] and two distinct vertices [ ] and [ ] are adjacent if and only if [ ] [ ] 0. In this paper, we try to establish some connections between ring theory and graph theory by studying the thickness of the line graph of the intersection graph of ideals of some rings. Here we obtain some bounds for the thickness, outerthickness and genus of the line graph of [ ], [ ]. We also study some results on the thickness and outerthickness of [ ]. Finally we determine the values of [ ] for which the graph [ ] is Eulerian and Hamiltonian.

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