AbstractLetGbe a simple undirected graph which haspvertices and is rooted atx.Informally, the rotation numberh(G, x)of this rooted graph is the minimum number of edges in ap‐vertex graphF, such that for each vertexvofF, there exists a copy ofGinFwith the rootxatv.In this paper, we calculate a lower bound for the rotation number of the graph which is the disjoint union of circuitsCk,Cewhere 4 ⩽k<⩽, give infinite classes where this bound is exact, and obtain classes of rotation numbers for the cas