Abstract: For natural numbers n,m,i∈N, let K_i be an i-vertex complet e graph, K_n is the complementay graph of graph K_n, St(m) represents a m+1-vertex star tree, T_n is a n-vertex tree, P_{n is a n-vertex path, P2∨Kn is the join graph of P2 and Kn. The present paper presents two kinds of unconne cted graphs (P2∨Kn)∪St(m) and (P2∨K}n)∪T_n, and proves that the two kinds of graphs are graceful graph s when n≥2.

Key words: simple graph, unconnectd graph, graceful graph