The relationships between inner dual, dualist, sextet dualist, antisextet dualist graphs and excised internal structures are fully delineated. It is proven that the antisextet dualist uniquely characterizes all strain-free benzenoids. At the same time, it is shown that the excised internal structure and dualist graph of the retro-leapfrog of all strain-free total resonant sextet (TRS) benzenoids correspond to their antisextet dualist and sextet dualist, respectively.