Document Type : Original Manuscript


Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran.


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 $F \cap E \neq \{1\}$. We denote this graph by $\mathcal{G}$ $(L)$. The basic properties and possible structures of $\mathcal{G}$ $(L)$ are studied. Moreover, we characterize the planarity of $\mathcal{G}$ $(L)$.


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