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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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Extinction and positivity of the solutions of the heat equations with absorption on networks
TL;DR: In this article, a discrete version of the following semilinear heat equation with absorption was proposed, which is known as ω-heat equations with absorption on a network, and it was proved that the asymptotic behaviors of the solutions u(x,t) as t tends to +∞ strongly depend on the sign of q−1.
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Spectral analogues of Erd\H{o}s' and Moon-Moser's theorems on Hamilton cycles
Binlong Li,Bo Ning +1 more
TL;DR: In this paper, the spectral analogies of Erdős' and Moon-Moser's Hamilton cycles in balanced bipartite graphs are presented, and the maximum (signless Laplacian) spectral radius of graphs in the class of non-Hamiltonian graphs of order $n$ and minimum degree at least $k is determined.
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The rank of a graph after vertex addition
TL;DR: The problem of determining the exact effect of adding a single vertex to a graph is more difficult, since the number of edges that can be added with this vertex is variable as mentioned in this paper.
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Some results on the index of unicyclic graphs
TL;DR: In this paper, the authors identify in some classes of unicyclic graphs (of fixed order and girth) those graphs whose index, i.e., the largest eigenvalue, is maximal.
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“Crowns”, and aromatic sextets in primitive coronoid hydrocarbons
TL;DR: In this article, a type of graphs derived from a cycle and associated with primitive coronoids are referred to as "crowns" and the characteristic polynomials of crowns are studied.