A convex characterization of the graphs of the dodecahedron and icosahedron

Let Γ be a 3-polytopal graph such that every face of Γ is convex. We prove that if the set of proper convex subgraphs of Γ is equal to the set of proper convex subgraphs of the dodecahedron (resp. icosahedron), then Γ is isomorphic to the dodecahedron (resp. icosahedron). © 1984.SCOPUS: ar.jinfo:eu-repo/semantics/publishe