Polychromatic polynomials


We refine the polychromate defined by Brylawski (J. Combin. Theory Ser. B 30 (1981) 233-246) to a graph invariant that takes account of a root vertex. Using the multiplicative structure that results, we show that this rooted polychromate distinguishes all non-isomorphic rooted trees. We also define an invariant finer than the polychromate - the strong polychromate - and conjecture that this invariant uniquely identifies almost all graphs. © 2000 Elsevier Science B.V. All rights reserved.

Publication Title

Discrete Mathematics