A linear descriptor for conceptual graphs and a class for polynomial isomorphism test

Abstract

The isomorphism problem is not known to be NP-complete nor polynomial. Yet it is crucial when maintaining large conceptual graphs databases. Taking advantage of conceptual graphs specificities, whenever, by means of structural functions, a linear order of the conceptual nodes of a conceptual graph G can be computed as invariant under automorphism, a descriptor is assigned to G in such a way that any other conceptual graph isomorphic to G has the same descriptor and conversely. The class of conceptual graphs for which the linear ordering of the conceptual nodes succeeds is compared to other relevant classes, namely those of locally injective, C-rigid and irredundant conceptual graphs. Locally injective conceptual graphs are proved to be irredundant, thus linearly ordered by the specialization relation.