On spectral bounds for cutsets

Authors:
J. A. Rodríguez;A. Gutiérrez;J. L. A. Yebra
Affiliations:
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Campus Nord, c/. Gran Capita, s/n Modul C3, 08034 Barcelona, Spain;Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Campus Nord, c/. Gran Capita, s/n Modul C3, 08034 Barcelona, Spain;Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Campus Nord, c/. Gran Capita, s/n Modul C3, 08034 Barcelona, Spain
Venue:
Discrete Mathematics
Year:
2002

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Abstract

Let Γ be a simple and connected graph. A k-vertex separator [k-edge separator] is a subset of vertices [edges] whose deletion separates the vertex [edge] set of Γ into two parts of equal cardinality, that are at distance greater than k in Γ. Here we investigate the relation between the cardinality of these cutsets and the laplacian spectrum of Γ. As a consequence of the study, we obtain the well-known lower bounds for the bandwidth and the bipartition width of a graph.