Abstract: The present paper deals with the gracefulness of three kinds of unconnected graphs ((P₁∨P_n)∪G_r,(P₁∨P_n)∪(P₃∨_r) and W_n∪St(m), and proves the following results： for positive integers n and m, let s=［n/2］, r=s-1, G_r be a graceful graph with redges, if n≥4, then the unconnected graphs (P₁∨P_n)∪G_r,(P₁∨P_n)∪(P₃∨_r) are both graceful graphs； if n≥3andm≥s, then the unconnected graph W_n∪St(m) is a graceful graph, where P_n is an nvertex path, K_n is an nvertex complete graph, nis the complement of graph K_n, graph G₁∨G₂ is the join graph of G₁ and G₂, W_nis an (n+1)vertex wheel graph and St(m)is an (m+1) vertex star tree.

Key words: graceful graph, graceful label, unconnected graph