Among graph theorists, the search for a short list of easily computed invariants sufficient to distinguish nonisomorphic graphs is something of a quest. Ninteenth century linear algebraists had a similar quest: To find a short list of easily computed invariants sufficient to distinguish dissimilar n-by-n matrices. The "holy grail" in that case turned out to consist of n polynomials, of which the characteristic polynomial is one. The talk involves an analogous list of relatively unexplored graph polynomials.

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