Strictly chordal graphs: Structural properties and integer Laplacian eigenvalues

Abstract

In this paper, we establish the relation between classic invariants and integer Laplacian eigenvalues of strictly chordal graphs, pointing out how their computation can be efficiently implemented. We review results concerning general graphs showing that the number of universal vertices and the degrees of twins provide integer Laplacian eigenvalues and their respective multiplicities. For strictly chordal graphs, we show new results about integer Laplacian eigenvalues which are directly related to particular vertex sets of the graph.