Laplace eigenvalues of graphs—a survey

TL;DR: A survey of the known results on eigenvalues of Cayley graphs and their applications can be found in this article, together with related results on Cayley digraphs and generalizations of the Cayley graph.

TL;DR: This study performs a statistical analysis of real data sets, representing the topology of different real-world networks, and suggests that the set of commonly used measures is too extensive to concisely characterize the topologies of complex networks.

TL;DR: This paper considers the nonexistence of graphs whose Laplacian matrix LG has an integral spectrum consisting of simple eigenvalues only in the range 0,...,n, and shows that for sufficiently large n such graphs do not exist.

TL;DR: In the management of large enterprise communication networks, it becomes difficult to detect and identify causes of abnormal change in traffic distributions when the underlying logical topology is unknown.

TL;DR: In this article, the authors introduce algebraic graph theory and show that the spectrum of a graph can be modelled as a graph graph, and the spectrum can be represented as a set of connected spanning trees.

TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.

TL;DR: It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and a well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases.

TL;DR: In this paper, it is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph.