Abstract The complexity of graph isomorphism ( GraphIso ) is a famous problem in computer science. For graphs G and H, it asks whether they are the same up to relabeling vertices. In 1981, Lubiw proved that list restricted ListIso NP -complete: for each u ∈ V , we given L ⊆ H possible images u. After 35 years, revive study this consider which results can be modified solve . We prove: 1) Under c...