Historical Outline
Spectral graph theory emerged in the 1950s and 1960s. Besides graph theoretic research on the relationship between structural and spectral properties of graphs, another major source was research in quantum chemistry, but the connections between these two lines of work were not discovered until much later. The 1980 monograph Spectra of Graphs by Cvetković, Doob, and Sachs summarised nearly all research to date in the area. In 1988 it was updated by the survey Recent Results in the Theory of Graph Spectra. The 3rd edition of Spectra of Graphs (1995) contains a summary of the further recent contributions to the subject.
Recent research is on the following subjects, among others:
- energy of graphs (the sum of the eigenvalues)
- Colin de Verdière-type invariants
- Laplacian matrix
- isoperimetric problems
- ergodicity
Read more about this topic: Spectral Graph Theory
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