scispace - formally typeset
Open AccessBook

Spectra of graphs : theory and application

Reads0
Chats0
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

Citations
More filters
Posted Content

On a Conjecture about Tricyclic Graphs with Maximal Energy

TL;DR: For a given simple graph G, the energy of G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix, which was defined by I. Gutman as discussed by the authors.
Journal ArticleDOI

Skew Spectra of Oriented Graphs

TL;DR: It is proved that (i) $Sp_S( G^{\sigma} ) = {\bf i} Sp(G)$ for some orientation $\sigma$ if and only if $G$ is bipartite, and (ii) $ Sp_S (G) = {\BF i) for any orientation $sigma” if andonly if G is a forest, where ${\bf i=\sqrt{-1}$.
Journal ArticleDOI

The PI index of product graphs

TL;DR: Using this formula, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed and the PI indices of C 4 nanotubes and nanotori are computed.
Posted Content

Random Field Models for Fitness Landscapes

TL;DR: This paper characterize isotropic random fields on finite graphs in terms of their Fourier series expansions and investigates the relation between the covariance matrix of the random field model and the correlation structure of the individual landscapes constructed from this random field.
Journal Article

On the distance spectra of some graphs

TL;DR: In this article, a pair of D-equienergetic bipartite graphs on 24 t, t ≥ 3, vertices is constructed, and the D-spectra of some graphs and their D-energies are calculated.