Developments in the theory of graph spectra
From MaRDI portal
Publication:4723771
DOI10.1080/03081088508817683zbMath0615.05039OpenAlexW1983949019MaRDI QIDQ4723771
Michael Doob, Dragos Cvetković
Publication date: 1985
Published in: Linear and Multilinear Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03081088508817683
eigenvectorsadjacency matrixroot systemsinfinite graphsleast eigenvaluegraph spectragraph polynomialsShannon capacity problemspectra of random graphs
Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)
Related Items
A study of eigenspaces of graphs ⋮ Spectra of unicyclic graphs ⋮ On the Laplacian Eigenvalues and Metric Parameters of Hypergraphs ⋮ Walk generating functions and spectral measures of infinite graphs ⋮ From local adjacency polynomials to locally pseudo-distance-regular graphs ⋮ Laplacian spectra and spanning trees of threshold graphs ⋮ The characteristic polynomials of modified graphs ⋮ Constructing trees with given eigenvalues and angles ⋮ Data Analytics on Graphs Part I: Graphs and Spectra on Graphs ⋮ Star partitions and the graph isomorphism problem ⋮ Tricylic hamiltonian graphs with minimal index ⋮ On the geometry and Laplacian of a graph ⋮ Some aspects of the development of linear algebra in the last sixty years ⋮ The local spectra of regular line graphs ⋮ A geometrical characterization of strongly regular graphs ⋮ On pseudo-distance-regularity ⋮ Minimal Euclidean representations of graphs ⋮ The change in index of a graph resulting from the attachment of a pendant edge ⋮ The laplacian matrix of a graph: unimodular congruence ⋮ The alternating and adjacency polynomials, and their relation with the spectra and diameters of graphs ⋮ Coalescing Fiedler and core vertices ⋮ Characteristic vertices of trees* ⋮ Characteristic vertices of trees* ⋮ Some results on graph spectra ⋮ The Local Spectra of Line Graphs ⋮ Laplacian matrices of graphs: A survey ⋮ A general method to obtain the spectrum and local spectra of a graph from its regular partitions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Constructing cospectral graphs
- On spectral characterization and embeddings of graphs
- Permanent of the Laplacian matrix of trees and bipartite graphs
- A table of connected graphs on six vertices
- Permanental roots and the star degree of a graph
- Discrete hyperbolic geometry
- A note on cospectral graphs
- Feasibility conditions for the existence of walk-regular graphs
- The expected eigenvalue distribution of a large regular graph
- Permanental polynomials of graphs
- Graphs with eigenvalues at least - 2
- Hermite polynomials and a duality relation for matchings polynomials
- The second largest eigenvalue of a tree
- On the asymptotic behaviour of the spectra of non-symmetric random \((0,1)\) matrices
- The spectrum of an infinite graph
- A surprising property of the least eigenvalue of a graph
- Recent results in the theory of graph spectra
- On a general class of graph polynomials
- An introduction to matching polynomials
- Line graphs, root systems, and elliptic geometry
- Spectral conditions for the reconstructibility of a graph
- Spektren periodischer Graphen
- Strongly regular graphs with smallest eigenvalue -m
- Matching behaviour is asymptotically normal
- Theory of monomer-dimer systems
- On the theory of the matching polynomial
- Matchings and walks in graphs
- Generalized line graphs
- A new graph product and its spectrum
- On the Shannon capacity of a graph
- Generalized Matrix Functions and the Graph Isomorphism Problem
- The electronic structure of conjugated systems I. General theory