zbMATH — the first resource for mathematics

The Laplacian spectrum of graphs. (English) Zbl 0840.05059
Alavi, Yousef (ed.) et al., Graph theory, combinatorics, and applications, Vol. 2. Proceedings of the sixth quadrennial international conference on the theory and applications of graphs held at Western Michigan University, Kalamazoo, MI, USA, May 30-June 3, 1988. New York: John Wiley & Sons, Inc. Wiley-Interscience Publication. 871-898 (1991).
Summary: 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 \(\lambda_2\) 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.
For the entire collection see [Zbl 0787.05004].

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)