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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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Ordering of Hückel trees according to minimal energies
TL;DR: In this article, the ordering of Huckel trees according to their minimal energies is investigated by means of a quasi-ordering relation. But it is not shown that the order of the trees obtained in this paper is the same as that of Li, who obtained the first 2 n - 10 - [ ( 1 + ( - 1 ) n ] / 2 trees in the increasing order of their energies within the class under consideration for n ⩾ 13, where 2 n is the vertex number of the tree.
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Spectral recognition of graphs
TL;DR: A survey of graph spectral recognition techniques used in computer sciences and the notion of spectral distance enables the design of various meta-heuristic algorithms for constructing graphs with a given spectrum (spectral graph reconstruction).
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Faber--Krahn type inequalities for trees
Türker Bıyıkoğlu,Josef Leydold +1 more
TL;DR: The Faber-Krahn theorem also holds for other classes of (not necessarily regular) trees, for example for trees with the same degree sequence, and the resulting trees possess a spiral like ordering of their vertices, i.e., are ball approximations as discussed by the authors.
Maximum Energy Trees with One Maximum and One Second Maximum Degree Vertex
TL;DR: In this paper, the authors considered the general case and characterized the maximum energy trees with one maximum degree vertex and another second maximum degree node and showed that these trees are the same as the trees with two maximum degree vertices.
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More about singular line graphs of trees
TL;DR: In this paper, the authors studied trees whose line graphs are singular and gave new results including the computer search which covers the trees with at most twenty vertices, and proved that the tree with the smallest number of vertices is singular.