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This work presents an approach to evaluate the exact value of the fractaldimension of the cutting path $d^{CP}_f$ on hierarchical structures with finiteorder of ramification. This represents the first renormalization grouptreatment of the universality class of watersheds. By making use of theself-similar property, we show that $d^{CP}_f$ depends only on the averagecutting path (CP) of the first generation of the structure. For the simplestWheastone hierarchical lattice (WHL), we present a mathematical proof. For alarger WHL structure, the exact value of $d^{CP}_f$ is derived based on ancomputer algorithm that identifies the length of all possible CP's of the firstgeneration.

Exact evaluation of the cutting path length in a percolation model on a hierarchical network