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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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On unicyclic conjugated molecules with minimal energies
TL;DR: In this paper, the authors studied the graph with minimal and second minimal energies in U(k) where k ≥ 0 and k ≥ 2, respectively, and proposed a conjecture on the graph having minimal energy in u(k).
Upper Bounds for the Energy of Graphs
TL;DR: The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. In as mentioned in this paper, the authors present some new upper bounds for E (G )i n ter m so f nu mber of vertices, number of edges, clique number, minimum degree, and the first Zagreb index.
On Harary Matrix, Harary Index and Harary Energy
Zhihui Cui,Bolian Liu +1 more
TL;DR: In this paper, some results about eigenvalues of Harary matrix are obtained, then by these results, some bounds of HarARY index are obtained.
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Topological Ring-Currents in Condensed Benzenoid Hydrocarbons*
TL;DR: Topological ring-currents are defined as being π-electron ring current intensities in condensed, benzenoid hydrocarbons that are calculated by the simplest Hiickel-London-Pople-McWeeny method, and expressed as a ratio to the corresponding ring current intensity calculated, by the same method, for benzene as discussed by the authors.
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On graphs whose signless Laplacian index does not exceed 4.5
TL;DR: In this article, Cvetkovic et al. investigated the properties of Q -spectra of graphs, especially for the limit points of the signless Laplacian.