Atena Tahmasbpour Meikola - Department of mathematics. Islamic Azad University, Central Tehran Branch, Iran

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.

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