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
Journal ArticleDOI

Bounds on the (Laplacian) spectral radius of graphs

TL;DR: The spectral radius of a graph is the largest eigenvalue of adjacency matrix of the graph and its Laplacian spectral radius, which is the difference of the diagonal matrix of vertex degrees and the adjACency matrix as mentioned in this paper.
Journal ArticleDOI

Resistance distance and Kirchhoff index of R -vertex join and R -edge join of two graphs

TL;DR: The resistance distances and the Kirchhoff index of G 1 { v } G 2 and G 1{ e} G 2 respectively are formulated.
Journal ArticleDOI

Offensive r-alliances in graphs

TL;DR: It is shown that the problem of finding optimal (global) offensive r-alliances is NP-complete and several tight bounds on @c"r^o(G) are obtained.
Journal ArticleDOI

Spectral distances of graphs

TL;DR: In this article, the spectral distance σ (G 1, G 2 ) between n vertex graphs G 1 and G 2 is defined by σ(G 1, G 2) = ∑ i = 1 n | λ i ( G 1 ) - λ I ( G 2 ), where i is the number of vertices in the graph.
Journal ArticleDOI

Viral conductance: Quantifying the robustness of networks with respect to spread of epidemics

TL;DR: A novel measure, viral conductance (VC), to assess the robustness of complex networks with respect to the spread of SIS epidemics, which incorporates the fraction of infected nodes at steady state for all possible effective infection strengths.