Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#Let G and H be 2-connected 2-isomorphic graphs with n nodes. Whitney's 2-isomorphism theorem states that G may be transformed to a graph G* isomorphic to H by repeated application of a simple operation, which  will term “switching”.  present a proof of Whitney's theorem that is much shorter than the original one, using a graph decomposition by Tutte. The proof also establishes a surprisingly small upper bound, namely n-2, on the minimal number of switchings required to derive G* from G. The bound is sharp in the sense that for any integer N there exist graphs G and H with n ≥ N nodes for which the minimal number of switchings is n-2.
['Klaus Truemper']
I am writing a research paper on a idea On Whitney's 2-isomorphism theorem for graphs
[{"from": "human", "value": "I am writing a research paper on a idea On Whitney's 2-isomorphism theorem for graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#Let G and H be 2-connected 2-isomorphic graphs with n nodes. Whitney's 2-isomorphism theorem states that G may be transformed to a graph G* isomorphic to H by repeated application of a simple operation, which  will term \u201cswitching\u201d.  present a proof of Whitney's theorem that is much shorter than the original one, using a graph decomposition by Tutte. The proof also establishes a surprisingly small upper bound, namely n-2, on the minimal number of switchings required to derive G* from G. The bound is sharp in the sense that for any integer N there exist graphs G and H with n \u2265 N nodes for which the minimal number of switchings is n-2."}]