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

In this paper, are introduced two new types of graphs of an MV- algebra (𝐴, +,⊙,∗, ۰, 𝐼) bybinary operations + and ⊙ which are denoted by Δ(𝐴) and 𝛱(𝐴), respectively. Also, byutilizing of concepts annihilator, binary operations + and ⊙, we construct two kinds ofgraphs of an MV- algebra (𝐴, +,⊙,∗, ۰, 𝐼) which are denoted by Ф(𝐴) and 𝛹(𝐴),respectively. Furthermore, by means of binary operation +, unary operation ∗, one type ofgraph an MV- algebra (𝐴, +,⊙,∗, ۰, 𝐼), is defined, denoted by Ɵ(𝐴). Then, fundamentalproperties of graph theory such as connectivity, regularity, planarity on the structure of thesegraphs are investigated. In addition, necessary condition is found for both Ф(𝐴) and 𝛹(𝐴)to be star graphs. Finally, the relationship between these five kinds of graphs is discussed

MV- lgebra, Connectedgraph, Clique, Girth,Diameter.