  The rotational dimension is a minor monotone graph invariant related to the
dimension of an Euclidean space containing a spectral embedding corresponding
to the first nonzero eigenvalue of the graph Laplacian, which is introduced by
G\"oring, Helmberg and Wappler. In this paper, we study rotational dimensions
of graphs which contain large complete graphs. The complete graph is
characterized by its rotational dimension. It will be a obtained that a chordal
graph may be made large while keeping the rotational dimension constant.
