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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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Journal ArticleDOI
On the (signless) Laplacian spectral characterization of the line graphs of lollipop graphs
Guangquan Guo,Guoping Wang +1 more
TL;DR: In this paper, it was shown that all line graphs L (H g, k n ) of lollipop graphs are determined by their signless Laplacian spectrum.
Journal ArticleDOI
A unified approach to the first derivatives of graph polynomials
Xueliang Li,Ivan Gutman +1 more
TL;DR: It is proved that d dx P(G,x)= ∑ v∈V(G) P (G−v,x) .
Proceedings ArticleDOI
Robustness of large networks
TL;DR: This work discusses how to describe large networks and argues that a stochastic approach is most appropriate, and studies the influence of the topology and of the link weight structure on the network's robustness.
Posted ContentDOI
Laplacian spectral characterization of some double starlike trees
Pengli Lu,Xiaogang Liu +1 more
TL;DR: In this paper, it was shown that a tree is called double star-like if it has exactly two vertices of degree greater than two and a tree can be determined by its Laplacian spectrum.
Nodal domains on graphs;how to count them and why?
Ram Band,Idan Oren,Uzy Smilansky +2 more
TL;DR: Several methods for counting nodal domains are presented in this paper, and their relevance as a tool in spectral analysis is discussed. But the focus of this paper is on nodal counts.