Titlebook: Laplacian Eigenvectors of Graphs; Perron-Frobenius and Türker Biyiko?u,Josef Leydold,Peter F. Stadler Book 2007 Springer-Verlag Berlin Heid

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Computational Experiments,ins may vary considerably depending on which eigenfunction from the .-dimensional eigenspace of . is chosen. Hence, given a fixed graph .(.) and an eigenvalue . of multiplicity . three questions immediately arise.

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Introduction, the adjacency spectrum to the spectrum of the closely related . [14, 35, 41, 85, 88, 137, 139]. In particular, Laplacian graph spectra are being investigated as a means of characterizing large “small world networks” and random graphs, see e.g. [33, 34, 119] for a few examples. For the most part, the theory is still concerned with the eigenvalues.

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Nodal Domain Theorems for Special Graph Classes,s. In this chapter we take a closer look to the situation for trees, cographs, and product graphs (in particular to the Boolean hypercube), where it is possible to derive improved upper and lower bounds.

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