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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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Seidel Integral Complete r-Partite Graphs
Ligong Wang,Guopeng Zhao,Ke Li +2 more
TL;DR: An upper bound and a lower bound for the smallest S-eigenvalue (or Seidel eigenvalue) of a complete multipartite graph are presented, from which infinitely many new classes of S-integral graphs are constructed.
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On the Laplacian and signless Laplacian spectrum of a graph with k pairwise co-neighbor vertices
TL;DR: In this paper, it was shown that the number of shared neighbors is a Laplacian and a signless LaplACian eigenvalue with multiplicity at least k−−−1.
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Laplacian coefficients and Zagreb indices of trees
TL;DR: A lower and an upper bound for are obtained in terms of the number of vertices, the Wiener, the first Zagreb and the forgotten indices of a simple and undirected graph, where T is a tree.
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Minimal webs in Riemannian manifolds
TL;DR: In this article, minimal isometric immersions of geometrized graphs (G, g) into Riemannian manifolds (N n,h ) are studied.
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Cospectrality of graphs
TL;DR: In this article, the cospectral distance between two nonisomorphic graphs with spectra is defined and a good upper bound on csncsn is given for special classes of graphs.