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About: Alon–Boppana bound     Goto   Sponge   NotDistinct   Permalink

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In spectral graph theory, the Alon–Boppana bound provides a lower bound on the second-largest eigenvalue of the adjacency matrix of a -regular graph, meaning a graph in which every vertex has degree . The reason for the interest in the second-largest eigenvalue is that the largest eigenvalue is guaranteed to be due to -regularity, with the all-ones vector being the associated eigenvector. The graphs that come close to meeting this bound are Ramanujan graphs, which are examples of the best possible expander graphs. Its discoverers are Noga Alon and .