Two graphs G and H with the same vertex set V are P4-isomorphic if there exists a permutation π on V such that, for all subsets S ⊆ V, S induces a chordless path on four vertices (denoted by P4) in G if and only if π(S) induces a P4 in H. This paper gives a classification of all graphs P4-isomorphic to a tree, respectively, a forest.
