gIs 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?

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.

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?

gIs 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?