Abstract：By employing the tree structure basis of coalgebra, an equivalent condition for coalgebra being isomorphic is achieved. The list of all isomorphism classes of 4-dimensional coalgebra is completed, and a general method for the classification of larger dimensional coalgebra is provided.
[1] ANDRUSKIEWITSCH N, NATALE S. Counting arguments for Hopf algebras of low dimension[J].Tsukuba Journal of Mathematics, 2001,25(1):187-201.
[2] BEATTIE M, D?SC?LESCU S. Hopf algebras of dimension 14[J].Journal of the London Mathematical Society,2004,69(1):65-78.
[3] FUKUDA D. Structure of coradical filtration and its application to Hopf algebras of dimension pq[J].Glasgow Mathematical Journal, 2008,50(2):183-190.
[4] MONTGOMERY S.Hopf Algebras and Their Actions on Rings[M]. Providence:American Mathematical Society, 1993.
2017, Vol. 44 
