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The main eigenvalues of a graph: A survey

Rowlinson Peter (University of Stirling, Mathematics and Statistics Group, Department of Computing Science and Mathematics, Stirling, Scotland)

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 connection 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.

Keywords: graph, harmonic graph, main eigenvalue, main angle, star partition