Laplacian eigenvalues and fixed size multisection Original Research Article

For a simple and non-directed graph, bounds on a weighted bisection are related to min and max laplacian eigenvalues, respectively. The purpose of this article is to extend this result to the multisection case where each partition among k has fixed size; both bounds rely on eigenvalues of a certain Gram matrix together with k smallest and k greatest laplacian eigenvalues. These bounds are compared with known ones.