Title of article :
A GRAPH ASSOCIATED TO FILTERS OF A LATTICE
Author/Authors :
Ebrahimi Atani ، Sh. Department of Mathematics - University of Guilan , Khoramdel ، M. Department of Mathematics - University of Guilan , Dolati Pish Hesari ، S. Department of Mathematics - University of Guilan , Nikmard Rostamalipour ، M. Department of Mathematics - University of Guilan
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 ∩ E ̸= {1}. We denote this graph by G(L). The basic properties and possible structures of G (L) are studied. Moreover, we characterize the planarity of G (L).
Keywords :
Lattice , Filter , Intersection graph
Journal title :
Journal of Algebraic Systems
Journal title :
Journal of Algebraic Systems
