by J. A. Makowsky and V. Rakita. On Weakly Distinguishing Graph Polynomials. Discrete Mathematics & Theoretical Computer Science (Oct. 31, 2018). arXiv: 1810.13300 [math.CO]. Submitted.

Let \(P\) be a graph polynomial. A graph \(G\) is \(P\)-unique if every graph \(H\) with \(P(G)=P(H)\) is isomorphic to \(G\). A graph \(H\) is a \(P\)-mate of \(G\) if \(P(G)=P(H)\) and \(H\) is not isomorphic to \(G\). It is a natural question to ask whether a given graph polynomial distinguishes graphs. Read more...

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