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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.

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New upper bounds for laplacian energy

Bo Zhou
TL;DR: In this paper, upper bounds and Nordhaus-Gaddum-type results for the Laplacian energy were obtained in terms of the number of vertices and the best possible.
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A relation between the multiplicity of the second eigenvalue of a graph laplacian, courant's nodal line theorem and the substantial dimension of tight polyhedral surfaces ∗

TL;DR: In this article, a relation between the multiplicity m of the second eigenvalue λ 2 of a Laplacian on a graph and a discrete analogue of Courant's nodal line theorem is discussed.
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Families of line-graphs and their quantization

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Spectral properties of the eccentricity matrix of graphs

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Remarks on hyperenergetic circulant graphs

TL;DR: In this paper, it was shown that for any given k1 < k2 < ··· < km almost all circulant graphs Ci(n, k1, k2,..., km) are hyperenergetic.