Matching number, Hamiltonian graphs and magnetic Laplacian matrices

In this article, we relate the spectrum of discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties graph: existence perfect matching and Hamiltonian cycle underlying graph. particular, give family spectral obstructions parametrised by potential for to be matchable (i.e., having matching) or cycle. We base our analysis special case preorder introduced in [8], use as control parameter.