Abstract
In this paper we extend the definition of pseudograceful graphs given by Frucht \3\ to all graphs G with vertex set V(G) and edge set E(G) such that \V(G)\less than or equal to \E(G)\ + 1 and we prove that if G is a pseudograceful graph, then G boolean ORKm,n is pseudograceful for rn, n greater than or equal to 2 and (In, n) not equal (2, 2), and is graceful for m, n greater than or equal to 2. This enables us to obtaill several new falnilies of graceful disconnected graphs.