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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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Book ChapterDOI
The Complexity of the Inertia
Thanh Minh Hoang,Thomas Thierauf +1 more
TL;DR: This paper shows that matrix stability is complete for PL and the inertia of symmetric matrices can be computed in PL and extends the result to some problems related to the inertia.
Book ChapterDOI
Spectra, Energy and Laplacian Energy of Strong Double Graphs
TL;DR: In this paper, the authors studied spectra, energy and Laplacian energy of the strong double graph SD(G) and derived a formula for the number of spanning trees in terms of the spectral energy of a graph.
Journal ArticleDOI
The line graphs of lollipop graphs are determined by their spectra
Jianfeng Wang,Shuning Shi +1 more
TL;DR: In this article, Zhang et al. showed that all line graphs of lollipop graphs are determined by their adjacency spectra, and employed the discriminant and the star value of a graph, whose relations were investigated in this paper.
Journal ArticleDOI
Perfect codes in Doob graphs
TL;DR: In this paper, it was shown that such codes that are linear over the Galois ring of Doob graphs exist only if and only if there exist integers (i.e., variables) > 0.i.d.