A GRAPH ASSOCIATED TO FILTERS OF A LATTICE

Author(s):

Sh. Ebrahimi Atani , M. Khoramdel * , S. Dolati Pish Hesari , M. Nikmard Rostamalipour

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

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 $mathcal{G}$ $(L)$.

Keywords:

Lattice , Filter , Intersection graph

Language:
English
Published:
Journal of Algebraic Systems, Volume:10 Issue: 2, Winter-Spring 2023
Pages:
345 to 359
https://www.magiran.com/p2462089  
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