Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let $S$ be a subset of the units in ${\bf Z_n}$.  Let ${\Gamma}$ be a circulant graph of order $n$ (a Cayley graph of ${\bf Z_n}$) such that if $ij\in E({\Gamma})$, then $i - j$ (mod $n$) $\in S$.  Toida conjectured that if $\Gamma'$ is another circulant graph of order $n$, then ${\Gamma}$ and ${\Gamma '}$ are isomorphic if and only if they are isomorphic by a group automorphism of ${\bf Z_n}$  ,  prove that Toida's conjecture is true.   further prove that Toida's conjecture implies Zibin's conjecture, a generalization of Toida's conjecture.
['Edward Dobson', 'Joy Morris']
I am writing a research paper on a idea Toida's Conjecture is True
[{"from": "human", "value": "I am writing a research paper on a idea Toida's Conjecture is True"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let $S$ be a subset of the units in ${\\bf Z_n}$.  Let ${\\Gamma}$ be a circulant graph of order $n$ (a Cayley graph of ${\\bf Z_n}$) such that if $ij\\in E({\\Gamma})$, then $i - j$ (mod $n$) $\\in S$.  Toida conjectured that if $\\Gamma'$ is another circulant graph of order $n$, then ${\\Gamma}$ and ${\\Gamma '}$ are isomorphic if and only if they are isomorphic by a group automorphism of ${\\bf Z_n}$  ,  prove that Toida's conjecture is true.   further prove that Toida's conjecture implies Zibin's conjecture, a generalization of Toida's conjecture."}]