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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 least distance eigenvalue of a graph
TL;DR: In this article, the least distance eigenvalue of a connected graph G with n vertices was determined and all the graphs with λ n ∈ [ − 2.383, 0 ] were determined.
Proceedings ArticleDOI
Network Density of States
TL;DR: In this article, the spectral density of real-world graphs is computed using tools developed in condensed matter physics and adapted to handle the spectral signatures of common graph motifs, and the resulting methods are highly efficient, as illustrate by computing spectral densities for graphs with over a billion edges on a single compute node.
On the origin of two degree-based topological indices
TL;DR: In this article, the authors analyze the way how these invariants were conceived in the 1970s and clarify some missing details, where the first Zagreb index M1 = P x2V (G) d(x) 2 and the second Zag Croatia index M2 = p xy2E(G)d(x)-d(y), where d is the degree of the vertex x ∈ V (G).
Journal ArticleDOI
Equienergetic self-complementary graphs
G. Indulal,Ambat Vijayakumar +1 more
TL;DR: In this article, equienergetic self-complementary graphs on p vertices for every p = 4k, k ⊆ 2 and p = 24t + 1, t ⩾ 3 are constructed.
Journal ArticleDOI
Constructing pairs of equienergetic and non-cospectral graphs
TL;DR: This work characterize the connected graphs G for which the product and the cartesian product of G and K 2 are equienergetic non-cospectral graphs and extends Balakrishnan’s result.