Classification of vertex-transitive cubic partial cubes

Partial cubes are graphs isometrically embeddable into hypercubes. In this paper it is proved that every cubic, vertex-transitive partial cube is isomorphic to one of the following graphs: K2ƒC2n, for some n ≥ 2, generalized Petersen graph G(10, 3), permutahedron, truncated cuboctahedron, or truncated icosidodecahedron. This complete classification of cubic, vertex-transitive partial cubes, a family that includes all cubic, distance-regular partial cubes (Weichsel, 1992), is a generalization of results of Brešar et. al. from 2004 on cubic mirror graphs, and a contribution to the classification of all cubic partial cubes.