Distance 2-domination in prisms of graphs.

A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u is an element of (V (G)- D) and D is at most two. Let gamma(2)(G) denote the size of a smallest distance 2 - dominating set of G. For any permutation pi of the vertex set of G, the prism of G with respect to pi is the graph pi G obtained from G and a copy G' of G by joining u is an element of V(G) with v ' is an element of V (G') if and only if v' = pi (u). If gamma(2)(pi G) = gamma(2)(G) for any permutation pi of V(G), then G is called a universal gamma(2)- fixer. In this work we characterize the cycles and paths that are universal gamma(2)-fixers.