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Is the total graph associated to powers of cycles homeomorphic to powers of cycles themselves?

I think yes, because the total graph associated to cycles is homeomorphic to cycles(i think?)So, does the same apply to powers of cycles, i.e., can the graph and its total graph have same genus? Any hints? Thanks beforehand.

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  • $\begingroup$ How do you define homeomorphism? Like the Wikipedia definition? $\endgroup$
    – LeechLattice
    Commented Feb 18, 2019 at 8:14
  • $\begingroup$ @Bullet51 yes, the same way $\endgroup$
    – vidyarthi
    Commented Feb 18, 2019 at 8:58

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