The Gracefulness of a Class of New Chain Graph

A definition is given of the mi-circle chain graph with a handle and mi-circle chain graph without handle.The gracefulness of the two kinds of graphs when m1,m2,…,mn≡0(mod 4) is discussed.The graceful lablings are given.In addition,the graceful labelings when m1,…,mn≡0(mod 4),mn+1≡(mod 4) are given.