A GRAPH ASSOCIATED TO FILTERS OF A LATTICE | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 2، فروردین 2023، صفحه 345-359 اصل مقاله (183.67 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.10633.1526 | ||
| نویسندگان | ||
| Sh. Ebrahimi Atani؛ M. Khoramdel* ؛ S. Dolati Pish Hesari؛ M. Nikmard Rostamalipour | ||
| Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran. | ||
| چکیده | ||
| 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 $\mathcal{G}$ $(L)$. | ||
| کلیدواژهها | ||
| Lattice؛ Filter؛ Intersection graph | ||
| مراجع | ||
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