On gracefulness ofG∪K_(m_in_i)from i=1 to k
Wei Pan · Journal of Changchun Post and Telecommunication Institute · 2004
In order to improve the study of the gracefulness of the disconnected graph,for natural numbers k ,m_i ,n_i,a kind of unconnected graph∪ki=1K_(m_i,n_i) was given.Furthermore it was proved that when max{m_i ,n_i}≥3, min{m_i,n_i}≥2 (i =1,2,…,k),the graph ∪ki=1K_(m_i,n_i) is graceful and alternating graph. And it is spreading widely.Let G and G_i (i=1,2,…,k) be the graceful graphs, the graph G∪ni=1G_i(joined by disconnected graphs ) is a graceful graph for given conditions.And a way to make a union of many graceful graphs union for the graceful graph was given.