The Laplacian Spectrum of Graphs †
نویسنده
چکیده
The paper is essentially a survey of known results about the spectrum of the Laplacian matrix of graphs with special emphasis on the second smallest Laplacian eigenvalue λ2 and its relation to numerous graph invariants, including connectivity, expanding properties, isoperimetric number, maximum cut, independence number, genus, diameter, mean distance, and bandwidth-type parameters of a graph. Some new results and generalizations are added. † This article appeared in “Graph Theory, Combinatorics, and Applications”, Vol. 2, Ed. Y. Alavi, G. Chartrand, O. R. Oellermann, A. J. Schwenk, Wiley, 1991, pp. 871–898. ‡ The work supported in part by the Research Council of Slovenia, Yugoslavia. Part of the work was done while the author was a Fulbright Scholar at the Ohio State University, Columbus, Ohio.
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