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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.read more
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Sharp Bounds on the Spectral Radius and the Energy of Graphs
Huiqing Liu,Mei Lu +1 more
TL;DR: In this article, the largest eigenvalue of adjacency matrix of a simple graph of order n with degree sequence d1,d2,...,vn was derived in terms of (m)i or (t)i.
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The spread of unicyclic graphs with given size of maximum matchings
TL;DR: In this article, the authors determine the graphs with the largest and second largest spectral radius in U*(n,k), and the graph with the smallest spread in U(n,k).
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Integral trees with diameters 5 and 6
Ligong Wang,Xueliang Li +1 more
TL;DR: The problem of finding integral trees of diameters 5 and 6 is equivalent to the problem of solving some Diophantine equations and the discovery of these integral trees is a new contribution to the search for such trees.
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On Mixed Graphs Whose Hermitian Spectral Radii are at Most 2
TL;DR: A sufficient condition is given which can make Hermitian spectral radius of a connected mixed graph strictly decreasing when an edge or a vertex is deleted, and all mixed graphs with Hermitan spectral radii at most 2 and with no cycle of length 4 in their underlying graphs are characterized.
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Distance between spectra of graphs
TL;DR: In this paper, it was shown that there is no constant upper bound on |e−e′|≤3e|e− e′| ≤1 In particular, for graphs G and G′G′, we have |e −e′ |≤1