Laplace eigenvalues of graphs—a survey

TL;DR: In this paper, lower and upper bounds for the signless Laplacian radius q 1 of a connected irregular graph were given. And they were shown that q 1 > 4 e n + ( Δ - δ ) 2 2 n Δ and q 1 2 Δ - 1 n ( d - 1 4 ) hold, where d is the diameter of G.

TL;DR: In this paper, the authors describe the graphs having the property that adding a particular edge will result in exactly two Laplacian eigenvalues increasing by 1 and the other eigen values remaining fixed.

TL;DR: In this article, the authors investigated adjacency spectrum, Laplacian spectrum, signless L 2 n, and detour spectrum of commuting and non-commuting graph of dihedral group D 2 n.

TL;DR: An overview of the development of Ramanujan graphs is given in this paper, where the authors explain how the subject started, the known explicit constructions of such graphs, the analogy between the spectral analysis of graphs and Riemannian manifolds, the distribution of the spectra of regular graphs, and an application from graph theory to modular forms.

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.