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

In this paper, first the notions of fuzzy filter and fuzzy LI- ideal in a lattice implication algebra (??,˅,˄,´,→,0,??) are defined. Then by means of congruence classes ≡???? and ≡???? on a lattice implication algebra (??,˅,˄,´,→,0,??) which induced by fuzzy filter and fuzzy LI-ideal, respectively, four types of graphs of lattice implication algebra (??,˅,˄,´,→,0,??), denoted by ??????(??),??????(??),??????(??) and ??????(??), respectively, are defined, some their interesting properties such as connectivity, chordality, planarity are presented.

Lattice implication algebra, Chordal graph, Connected graph, Clique, Planar graph, Girth, Diameter, Fuzzy filter, Fuzzy LI- ideal.