Defective chromatic polynomials determine the degree sequence of triangle-free graphs and path-subgraph counts N(P_j,T) for j=1-4 in trees, but nonisomorphic trees of order n≥9 exist with identical families for all d.
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Defective chromatic polynomials
Defective chromatic polynomials determine the degree sequence of triangle-free graphs and path-subgraph counts N(P_j,T) for j=1-4 in trees, but nonisomorphic trees of order n≥9 exist with identical families for all d.