Twelve Kinds of Graphs of Lattice Implication Algebras Based on Filter and LI- ideal

Authors : Atena TAHMASBPOUR MEİKOLA

Pages : 11-40

View : 14 | Download : 4

Publication Date : 2020-05-01

Article Type : Research Paper

Abstract :In this paper, at first we introduce the concepts of filter- annihilator, LI- ideal- annihilator, right- filter- annihilator, left- filter- annihilator, right- LI- ideal- annihilator, and left- LI- ideal- annihilator. Then by using of these concepts, are constructed six new types of graphs in a lattice implication algebrainsert ignore into journalissuearticles values(L,˅,˄,´,→,0,I); which are denoted by Ф_F insert ignore into journalissuearticles values(L);,Ф_A insert ignore into journalissuearticles values(L);,∆_F insert ignore into journalissuearticles values(L);,Σ_F insert ignore into journalissuearticles values(L);,∆_A insert ignore into journalissuearticles values(L);, and Σ_A insert ignore into journalissuearticles values(L);, respectively. Then basic properties of graph theory such as connectivity, regularity, and planarity on the structure of these graphs are investigated. Secondly, by utilizing of binary operations ⊕ and ⊗ we construct graphs Ψ_F insert ignore into journalissuearticles values(L); and Ψ_A insert ignore into journalissuearticles values(L);, respectively. Thirdly, via the binary operations ⊕ and ⊗, concept of annihilator we construct graphs Ω_F insert ignore into journalissuearticles values(L); and Ω_A insert ignore into journalissuearticles values(L);, respectively. Finally, by utilizing of binary operations ˄ and ˅, we construct graphs Υ_F insert ignore into journalissuearticles values(L); and Υ_A insert ignore into journalissuearticles values(L);, respectively, some their interesting properties are presented.
Keywords : Lattice implication algebra, Diameter, Chromatic number, Euler graph