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Characterizes structures and planarity of graphs associated with filters in lattices.
Let L be a lattice with the least element $0$ and the greatest element $1$. In this paper, we associate a graph to filters of L, in which the vertex set is being the set of all non-trivial filters of L, and two distinct vertices F and E are adjacent if and only if F ∩ E ≠ \1\. We denote this graph by G $(L)$. The basic properties and possible structures of G $(L)$ are studied. Moreover, we characterize the planarity of G $(L)$.
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Atani et al. (2023) studied this question.
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