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Algebraic methods in Graph Theory; the linear algebra method, graph homomorphisms, group theoretic methods (for example Cayley graphs), and graph invariants. For graph eigenvalue problems use the spectral-graph-theory tag. For strongly regular graphs use the strongly-regular-graph tag. For Kneser graphs use the kneser-graph tag.

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Graduate Schools for Graph Theory

Here's my (incomplete) list of recommendations based on my current knowledge of graph theory research. General: Rutgers, UCSD, Tel Aviv, Waterloo, McGill, Princeton, Yale, Eötvös Loránd University, …