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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 the number of spanning trees of some irregular line graphs
TL;DR: It is proved that if G is irregular, then t ( L ( G ′ ) ) = 2 m − n + 1 Δ m + s − n − 1 t ( G ) , where s is the number of vertices of degree one in G ‼ .
On Biregular Graphs whose Energy Exceeds the Number of Vertices
TL;DR: In this paper, the sufficient condition for E(G) ≥ n in the case of biregular graphs with no three of their quadrangles having a common vertex was established.
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Maximizing the spectral radius of k-connected graphs with given diameter ☆
TL;DR: In this paper, the authors generalize Hansen and Stevanovic's result to k-connected graphs of order n with diameter D and show that the graph with the largest spectral radius is the k-clique with the smallest adjacency matrix.
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Two-colorable graph states with maximal Schmidt measure
TL;DR: In this paper, it was shown that the graph operations called local complementation and switching form a transitive group acting on the set of all graph states of a given dimension, and that almost all two-colorable graph states have maximal Schmidt measure.
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Spectral distances of graphs based on their different matrix representations
Irena M. Jovanović,Zoran Stanić +1 more
TL;DR: Jovanovic et al. as discussed by the authors defined Laplacian and signless spectral distances and considered their relations to the spectral distances of graphs based on the adjacency matrix of graph.