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The main eigenvalues of a graph: a survey. (English) Zbl 1199.05241

Summary: We survey results relating main eigenvalues and main angles to the structure of a graph. We provide a number of short proofs, and note the connections with star partitions. We discuss graphs with just two main eigenvalues in the context of measures of irregularity, and in the context of harmonic graphs.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
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