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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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Graph spectral techniques in computer sciences
TL;DR: A survey of graph spectral techniques used in computer sciences consists of a description of particular topics from the theory of graph spectra independently of the areas of Computer science in which they are used.
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Counting cycles and finite dimensional Lp norms
TL;DR: It is proved that the complete graph is optimal in more ways than could be imagined and sharp bounds for the number of n-cycles in a finite graph are obtained.
Estimating the Wiener Index by Means of Number of Vertices, Number of Edges, and Diameter
Kinkar Ch. Das,Ivan Gutman +1 more
TL;DR: In this paper, lower and upper bounds on the Wiener index of connected graphs and of triangle-free graphs are obtained in terms of the number of vertices, number of edges, and diameter.
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Spectra of graph operations based on R-graph
TL;DR: In this article, the adjacency spectra of four types of graph operations on and involving the R-graph of a regular graph and an arbitrary graph were determined for each edge of the regular graph by adding a new vertex for each vertex and joining each new vertex to the end vertices of the corresponding edge.
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On the distance spectrum of distance regular graphs
Fouzul Atik,Pratima Panigrahi +1 more
TL;DR: In this article, it was shown that distance regular graphs with diameter d have at most d + 1 distinct D-eigenvalues, where d i j is the distance between ith and jth vertices of a simple connected graph G. The spectrum of the distance matrix is known as the distance spectrum or D-spectrum of G.