Embedding and the rotational dimension of a graph containing a clique

Abstract

The rotational dimension is a minor-monotone graph invariant related to the dimension of a Euclidean space containing a spectral embedding corresponding to the first nonzero eigenvalue of the graph Laplacian, which is introduced by Göring, 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 obtained that a chordal graph may be made large while keeping the rotational dimension constant.