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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 spectral characterizations of ∞-graphs
TL;DR: It is proved that all ~-graphs without triangles are determined by their Laplacian spectra and that all graphs, with one exception, areetermined by their signless Laplacan spectra.
Journal ArticleDOI
Computing the forgotten topological index of four operations on graphs
TL;DR: The first and second Zagreb indices for the four operations on graphs were studied by Deng et al. (2016) and the closed formulas for the F -index of four Operations on graphs are determined.
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In search of structural invariants
TL;DR: In this paper, the authors outline selected accomplishments of the past, show some current efforts and point to directions which may lead to further advancements in chemical graph theory, and suggest some current directions for further advancements.
Relation between energy and laplacian energy
TL;DR: For a graph G with n vertices and m edges, with ordinary spectrum λi,i = 1, 2,...,n, and with Laplacian spectrum μi,i =1, 2,...,n, the energy and the LaplACian energy are defined as E(G ) = n � i=1 |λi| and LE(G ), i = 1 |μi − 2m/n|, respectively as mentioned in this paper.
Journal ArticleDOI
On the spectral radius of trees with fixed diameter
Ji-Ming Guo,Jia-Yu Shao +1 more
TL;DR: In this article, the first d2+1 spectral radii of trees in the set T(n, d) (3 ⩽ d⩽ n − 4) were characterized.