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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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\ell_1 -Rigid Graphs
M. Deza,Monique Laurent +1 more
TL;DR: It is shown that many interesting graphs are ℓ1-rigid, i.e., that they admit an essentially unique such binary labeling in such a way that the Hamming distance between the binary addresses is the distance in the graph between the corresponding nodes.
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Some results on the Laplacian spectrum
Muhuo Liu,Bolian Liu +1 more
TL;DR: A sharp upper bound for the algebraic connectivity of a graph is obtained, and all the Laplacian integral unicyclic, bicyclic graphs are identified and determined by their LaPLacian spectra.
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The inertia and energy of distance matrices of complete k-partite graphs
TL;DR: In this article, the authors studied the inertia of complete k-partite graphs with n vertices and obtained the graphs with the maximum (resp. minimum) D-energy.
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The signless Laplacian spectral radius of bicyclic graphs with prescribed degree sequences
TL;DR: All extremal connected bicyclic graphs with the largest signless Laplacian spectral radius in the set of all connected bicyclIC graphs with prescribed degree sequences are characterized and the signlessLaplacians majorization theorem is proved to be true for connected bicyic graphs.
Journal Article
Laplacian Energy of Directed Graphs and Minimizing Maximum Outdegree Algorithms
TL;DR: In this paper, the authors derived two types of equations for simple directed graphs and symmetric directed graphs with n ≥ 2 vertices by considering out-degree of vertex, and enumerated the structure of directed graphs using the Laplacian energy concept.