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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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Journal ArticleDOI
Spectral gap for quantum graphs and their connectivity
TL;DR: In this article, the spectral gap for Laplace operators on metric graphs is investigated in relation to graph's connectivity, in particular what happens if an edge is added to (or deleted from) a graph.
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Improving the McClelland inequality for total π-electron energy
TL;DR: In this paper, the McClelland inequality was used to estimate the total π-electron energy (E) of a conjugated hydrocarbon by means of the number of carbon atoms (n) and carbon-carbon bonds (m), and it was shown that 2m/n+ (n−1)(2m−4m 2 /n 2 ) is a better upper bound for E.
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Networks in Conflict: Theory and Evidence from the Great War of Africa
TL;DR: In this article, the authors study from both a theoretical and an empirical perspective how a network of military alliances and enmities affects the intensity of a conflict and obtain a closed form characterization of the Nash equilibrium of the fighting game, and how the network structure affects individual and total fighting efforts.
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The minimal spectral radius of graphs with a given diameter
E.R. van Dam,Robert E. Kooij +1 more
TL;DR: In this paper, the authors considered the problem of finding a connected graph on n nodes and a given diameter D has minimal spectral radius, where D is the maximum number of hops between any pair of nodes in the graph.
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Eigenvalues and triangles in graphs
TL;DR: It is proved that every non-bipartite graph of order and size contains a triangle if one of the following is true: $(G) \ge \sqrt {m - 1} $ and $G
e {C_5} \cup (n - 5){K_1}$.