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

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 algebra(L,˅,˄,´,→,0,I) which are denoted by Ф_F (L),Ф_A (L),∆_F (L),Σ_F (L),∆_A (L), and Σ_A (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 (L) and Ψ_A (L), respectively. Thirdly, via the binary operations ⊕ and ⊗, concept of annihilator we construct graphs Ω_F (L) and Ω_A (L), respectively. Finally, by utilizing of binary operations ˄ and ˅, we construct graphs Υ_F (L) and Υ_A (L), respectively, some their interesting properties are presented.

Keywords

• Lattice implication algebra,Diameter,Chromatic number,Euler graph

Thanks

The author is grateful to the reviewers for many suggestions which improved the presentation of the paper.

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