Abstract. A vertex of a graph dominates itself and all its neighbours. A set S, subset of vertices of a graph G, dominates the graph G efficiently if every vertex of G is dominated by exactly one vertex of S. Mobius ladder M_n is a cubic graph obtained from the cycle on 2n vertices by adding a perfect matching connecting pairs of opposite vertices.

Using an algebraic approach based on lifts we prove that, a connected vertex-transitive cubic graph G on 2^m vertices does not admit efficient dominating set if and only if m≥3 and G is isomorphic to the Mobius ladder M_2^m-1.