A GRAPH ASSOCIATED TO FILTERS OF A LATTICE

Let L be a lattice with the least element ۰ and the greatest element ۱. 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 \{۱\}. 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).

کلیدواژه ها:

Lattice ، Filter ، Intersection graph