Discrimination power of graph measures based on complex zeros of the partial Hosoya polynomial

In this paper we define novel graph measures based on the complex zeros of the partial Hosoya polynomial. The kth coefficient of this polynomial, defined for an arbitrary vertex v of a graph, is the number of vertices at distance k from v. Based on the moduli of the complex zeros, we calculate novel graph descriptors on exhaustively generated graphs as well as on trees. We then evaluate the uniqueness of these measures, i.e., their ability to distinguish between non-isomorphic graphs. Detecting isomorphism for arbitrary graphs remains a challenging problem for which highly discriminating graph invariants are useful heuristics.