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

Year 2020, Volume: 17 Issue: 1, 11 - 40, 01.05.2020

Atena Tahmasbpour Meikola

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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