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Spectra of graphs : theory and application

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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Proceedings ArticleDOI

CLIPPER: A Graph-Theoretic Framework for Robust Data Association

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Polynomial reconstruction of signed graphs

TL;DR: In this article, the reconstruction problem of the characteristic polynomial of graphs from their polynomials was studied for graphs of order n > 2, and besides some general results, it was shown that the problem can be resolved within signed trees and unicyclic signed graphs, and also within disconnected signed graphs.
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On the spectral characterization of theta graphs

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Randić index and lexicographic order

TL;DR: In this paper, it was shown that the Randic index is monotone increasing over a well-ordered sequence of trees with unique branched vertices, where the degree of each vertex is determined by the number of vertices in the tree.
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Resolution of AutoGraphiX conjectures relating the index and matching number of graphs

TL;DR: In this article, the authors resolve conjectures of AutoGraphiX relating the index and the matching number of connected graphs, and show that these conjectures are not correct and propose a new index index for connected graphs.