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Spectra of graphs : theory and application
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TLDR
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.Abstract:
Introduction. Basic Concepts of the Spectrum of a Graph. Operations on Graphs and the Resulting Spectra. Relations Between Spectral and Structural Properties of Graphs. The Divisor of a Graph. The Spectrum and the Group of Automorphisms. Characterization of Graphs by Means of Spectra. Spectra Techniques in Graph Theory and Combinatories. Applications in Chemistry an Physics. Some Additional Results. Appendix. Tables of Graph Spectra Biblgraphy. Index of Symbols. Index of Names. Subject Index.read more
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Journal ArticleDOI
The spectrum and the signless Laplacian spectrum of coronae
Shu-Yu Cui,Gui-Xian Tian +1 more
TL;DR: In this paper, the M -coronal of a graph matrix M is introduced, where the matrix is associated with a graph in a prescribed way, and then it is used to compute the signless Laplacian spectrum of G 1 ∘ G 2 and G 1 ♢ G 2 in terms of the signedless L 1 spectrum of g 1 and g 2, respectively.
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The signless Laplacian spectral radius of graphs with given degree sequences
TL;DR: All extremal unicyclic graphs having the largest signless Laplacian spectral radius are obtained in the sets of all unicyCLic graphs of order n with a specified number of leaves or maximum degree or independence number or matching number.
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A computational study of graph partitioning
TL;DR: A numerical study on the use of eigenvalue-based techniques to find upper and lower bounds for the graph partitioning problem and shows that the techniques are very robust and consistently produce upper andLower bounds having a relative gap of typically a few percentage points.
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The generalized hierarchical product of graphs
TL;DR: The spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product are studied.
Journal ArticleDOI
Spectral Theory for Dynamics on Graphs Containing Attractive and Repulsive Interactions
Jared C. Bronski,Lee DeVille +1 more
TL;DR: This paper shows that the there are topological constraints on the index of the Laplacian matrix related to the dimension of a certain homology group, which gives bounds on the number of positive and negative eigenvalues.