Classification of Vertex‐Transitive Cubic Partial Cubes

Partial cubes are graphs isometrically embeddable into hypercubes. In this article, it is proved that every cubic, vertex‐transitive partial cube is isomorphic to one of the following graphs: , for , the generalized Petersen graph G (10, 3), the cubic permutahedron, the truncated cuboctahedron, or the truncated icosidodecahedron. This classification is a generalization of results of Bre?ar et  al. (Eur J Combin 25 (2004), 55–64) on cubic mirror graphs; it includes all cubic, distance‐regular partial cubes (P. M. Weichsel, Discrete Math 109 (1992), 297–306), and presents a contribution to the classification of all cubic partial cubes.