More rotation numbers for complete bipartite graphs

Let G be a simple undirected graph which has p vertices and is rooted at x. Informally, the rotation number h(G, x) of this rooted graph is the minimum number of edges in a p vertex graph H such that for each vertex v of H, there exists a copy of G in H with the root x at v. In this article we calculate some rotation numbers for complete bipartite graphs, and thus greatly extend earlier results of Cockayne and Lorimer.