Graphs with magnetic Schrodinger operators of low corank

摘要

Colin de Verdiere (1998, J. Combin. Theory, Ser. B. 74, 121-146) introduced the graph parameter v(G), which is defined as the maximal corank of any positive semidefinite magnetic Schrodinger operator fulfilling a certain transversality condition. He showed that for connected simple graphs, nu(G) less than or equal to 1 if and only if G is a tree. In this paper we characterize for k = 2, 3, the classes of graphs G with nu(G) less than or equal to k. (C) 2002 Elsevier Science (USA). [References: 13]