Geodesic
The Cayley Sum Graph of Ideals of a Lattice
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 2, pp. 217-230

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Let L be a lattice, ℑ(L) be the set of ideals of L and S be a subset of ℑ(L). In this paper, we introduce an undirected Cayley graph of L, denoted by Γ_L,S with elements of ℑ(L) as the vertex set and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of S such that I ∨ K = J or J ∨ K = I. We study some basic properties of the graph Γ_L,S such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of Γ_L,S.
Keywords: lattice, Cayley graph, ring graph, outerplanar graph 
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Afkhami, Mojgan; Hassankhani, Mehdi; Khashyarmanesh, Kazem. The Cayley Sum Graph of Ideals of a Lattice. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 2, pp. 217-230. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_2_a6/