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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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Combinatorial approach for computing the characteristic polynomial of a matrix
TL;DR: In this paper, the authors used the Coates digraph as a main tool to extend, in a combinatorial way, some well known results from the spectral graph theory on computing the characteristic polynomial of graphs.
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Connections between generalized graph entropies and graph energy
TL;DR: Some extremal properties of a class of generalized graph entropies are proved by using the graph energy and the spectral moments.
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Graphs with four distinct Laplacian eigenvalues
TL;DR: In this article, the authors investigate connected nonregular graphs with four distinct Laplacian eigenvalues and characterize all such graphs which are bipartite or have exactly one multiple Laplacey eigenvalue.
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Some remarks on Laplacian eigenvalues and Laplacian energy of graphs
TL;DR: In this article, some new bounds for the Laplacian eigenvalues and energy of some special types of the subgraphs of a graph G are presented, and some new assumptions for the energy of G are given.
Note on the Distance Energy of Graphs
TL;DR: In this article, the distance energy of a graph G is defined as the sum of the absolute values of the eigenvalues of the distance matrix of G. The distance matrix is defined to be defined as a function of the number of vertices and edges of G in the graph.