A Descent on Simple Graphs -- from Complete to Cycle -- and Algebraic Properties of Their Spectra
classification
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graphsalgebraiccompletecycledescentgraphlargesimple
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We investigate a descent on simple graphs, starting with the complete graph on $n$ vertices and ending up with the cycle graph by removing one edge after another. We obtain quantitative results showing that graphs with large diameter must have some eigenvalues of large algebraic degree.
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