Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  prove that regular graphs and graphs with @c=4 are not universal fixers.
['Alewyn P. Burger', 'Christina M. Mynhardt']
I am writing a research paper on a idea Regular graphs are not universal fixers
[{"from": "human", "value": "I am writing a research paper on a idea Regular graphs are not universal fixers"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  prove that regular graphs and graphs with @c=4 are not universal fixers."}]