Bipartite graphs are not universal fixers

For any permutation @p of the vertex set of a graph G, the graph @pG is obtained from two copies G^' and G^'' of G by joining u@?V(G^') and v@?V(G^'') if and only if v=@p(u). Denote the domination number of G by @c(G). For all permutations @p of V(G), @c(G)@?@c(@pG)@?2@c(G). If @c(@pG)=@c(G) for all @p, then G is called a universal fixer. We prove that graphs without 5-cycles are not universal fixers, from which it follows that bipartite graphs are not universal fixers.

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