Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Using hypergraph transversals it is proved that $\gamma_t(Q_{n+1}) = 2\gamma(Q_n)$, where $\gamma_t(G)$ and $\gamma(G)$ denote the total domination number and the domination number of $G$, respectively, and $Q_n$ is the $n$-dimensional hypercube. More generally, it is shown that if $G$ is a bipartite graph, then $\gamma_t(G \square K_2) = 2\gamma(G)$. Further,  show that the bipartiteness condition is essential by constructing, for any $k \ge 1$, a (non-bipartite) graph $G$ such that $\gamma_t(G\square K_2) = 2\gamma(G) - k$. Along the way several domination-type identities for hypercubes are also obtained.
['Jernej Azarija', 'Michael A. Henning', 'Sandi Klavžar']
I am writing a research paper on a idea Total) Domination in Prisms
[{"from": "human", "value": "I am writing a research paper on a idea Total) Domination in Prisms"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Using hypergraph transversals it is proved that $\\gamma_t(Q_{n+1}) = 2\\gamma(Q_n)$, where $\\gamma_t(G)$ and $\\gamma(G)$ denote the total domination number and the domination number of $G$, respectively, and $Q_n$ is the $n$-dimensional hypercube. More generally, it is shown that if $G$ is a bipartite graph, then $\\gamma_t(G \\square K_2) = 2\\gamma(G)$. Further,  show that the bipartiteness condition is essential by constructing, for any $k \\ge 1$, a (non-bipartite) graph $G$ such that $\\gamma_t(G\\square K_2) = 2\\gamma(G) - k$. Along the way several domination-type identities for hypercubes are also obtained."}]