Geodesic
Planarity of a spanning subgraph of~the~intersection graph of ideals of~a~commutative ring~II, Quasilocal Case
Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 117-143

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The rings we consider in this article are commutative with identity $1\neq 0$ and are not fields. Let $R$ be a ring. We denote the collection of all proper ideals of $R$ by $\mathbb{I}(R)$ and the collection $\mathbb{I}(R)\setminus \{(0)\}$ by $\mathbb{I}(R)^{*}$. Let $H(R)$ be the graph associated with $R$ whose vertex set is $\mathbb{I}(R)^{*}$ and distinct vertices $I, J$ are adjacent if and only if $IJ\neq (0)$. The aim of this article is to discuss the planarity of $H(R)$ in the case when $R$ is quasilocal.
Keywords: quasilocal ring, local Artinian ring, special principal ideal ring, planar graph. 
@article{ADM_2019_27_1_a11,
     author = {P. Vadhel and S. Visweswaran},
     title = {Planarity of a spanning subgraph of~the~intersection graph of ideals of~a~commutative {ring~II,} {Quasilocal} {Case}},
     journal = {Algebra and discrete mathematics},
     pages = {117--143},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a11/}
}
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P. Vadhel; S. Visweswaran. Planarity of a spanning subgraph of~the~intersection graph of ideals of~a~commutative ring~II, Quasilocal Case. Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 117-143. http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a11/