Graphs of Lattice Implication Algebras Based on Filter

In this paper, first is introduced the notion of congruence class ≡𝐹 on a lattice implicationalgebra (𝐿, ˅, ˄, ´, ۰, 𝐼) which is determined by filter. Then, by using of that, we constructtwo types of graphs of lattice implication algebra (𝐿, ˅, ˄, ´, ۰, 𝐼) are denoted by 𝛤𝐹 (𝐿) and𝛤𝐹 (𝐿). Then, fundamental properties of graph theory such as connectivity, regularity,chordality, planarity on the structure of those graphs are studied.

Keywords:

Lattice implication algebra , Filter , Connected Graph , Clique , Girth , Diameter , Planar Graph , ChordalGraph.