Abstract:In recent years, zero-divisor graph mainly uses the language and tools of graph theory to study and solve some research problems in algebra.For any finite local ring R, the algebraic structure of ring R is always a difficult problem.We study the algebraic properties of rings R whose zero-divisor graph Γ(R) has clique number five.Furthermore, we give the complete characterizations of the maximal ideal of the finite commutative local rings with ω(Γ(R))=5 and N()=5.