Domination of generalized Cartesian products

The generalized prism pi G of G is the graph consisting of two copies of G, with edges between the copies determined by a permutation pi acting on the vertices of G. We define a generalized Cartesian product G (sic) H that corresponds to the Cartesian product G square H when pi is the identity, and the generalized prism when H is the graph K(2). Burger, Mynhardt and Weakley [A.P. Burger, C.M. Mynhardt, W.D.Weakley, On the domination number of prisms of graphs, Discuss. Math. Graph Theory 24 (2) (2004) 303-318.] characterized universal doublers, i.e. graphs for which gamma(pi G) = 2 gamma(G) for any pi. In general gamma(G (sic) K(n)) <= n gamma(G) for any n >= 2 and permutation pi, and a graph attaining equality in this upper bound for all pi is called a universal multiplier. We characterize such graphs. (C) 2010 Published by Elsevier B.V.