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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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On bipartite graphs with small number of laplacian eigenvalues greater than two and three
TL;DR: In this article, the authors determined all connected bipartite graphs with exactly two Laplacian eigenvalues greater than two, and all graphs with at most three eigenvectors greater than three.
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Vertex PI indices of four sums of graphs
Shuhua Li,Guoping Wang +1 more
TL;DR: The explicit expressions for the vertex PI indices of four sums of two graphs in terms of other indices of two individual graphs are given, which correct the main results in a paper published in Ars Combin.
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On some forests determined by their Laplacian or signless Laplacian spectrum
Slobodan K. Simić,Zoran Stanić +1 more
TL;DR: The class of graphs whose each component is either a proper subgraph of some Smith graphs, or belongs to a precized subset of Smith graphs is considered, and those which are determined, or not determined, by Laplacian, or signless LaPLacian spectrum are classified.
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Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
TL;DR: In this paper, a continuous-variable analog to the Kitaev surface code using quantum harmonic oscillators on a two-dimensional lattice is described, which has the distinctive property of requiring only two-body nearest-neighbor interactions for its creation.
Journal ArticleDOI
Distance spectrum of Indu–Bala product of graphs
G. Indulal,R. Balakrishnan +1 more
TL;DR: The distance spectrum of G 1 ▾ G 2 is obtained in terms of the adjacency spectra of G1 and G 2 to obtain a new class of distance equienergetic graphs of diameter 3 and it is proved that the class of graphs K n ¯ ▾ K n + 1 ¯ has integral distance spectrum.