In this paper, structural properties of chordal graphs are studied, establishing a relationship between these structures and integer Laplacian eigenvalues. We present the characterization with equal vertex algebraic connectivities, by means vertices that compose minimal separators graph; we stablish sufficient condition for cardinality maximal clique to appear as an eigenvalue. Finally, review ...

We define the Laplacian for a general graph and then examine several isoperimetric inequalities which relate the eigenvalues of the Laplacian to a number of graphs invariants such as vertex or edge expansions and the isoperimetric dimension of a graph.

We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if and only if the manifold has a metric of positive scalar curvature. We show that the invariant does not increase under surgery of codimension at least three and we give lower and upper bounds in terms of the α-genus.