TY - JOUR ID - 2479 TI - A GRAPH ASSOCIATED TO FILTERS OF A LATTICE JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Ebrahimi Atani, Sh. AU - Khoramdel, M. AU - Dolati Pish Hesari, S. AU - Nikmard Rostamalipour, M. AD - Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran. Y1 - 2023 PY - 2023 VL - 10 IS - 2 SP - 345 EP - 359 KW - Lattice KW - Filter KW - Intersection graph DO - 10.22044/jas.2022.10633.1526 N2 - 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 $\mathcal{G}$ $(L)$. UR - https://jas.shahroodut.ac.ir/article_2479.html L1 - https://jas.shahroodut.ac.ir/article_2479_32018ff0f5780e323702b204f0d79d44.pdf ER -