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In this paper, we show the explicit formula of the recurrence relation for the Tower of Hanoi on the star graph with four vertices, where the perfect tower of disks on a leaf vertex is transferred to the central vertex. This gives the solution to the problem posed at the 17th International Conference on Fibonacci Numbers and Their Applications [11]. Then, the recurrence relation are generalized to include the ones for the original 4-peg Tower of Hanoi and the Star Tower of Hanoi of transferring the tower from a leaf to another. key words: Tower of Hanoi, four pegs, star graph, Frame-Stewart algorithm, recurrence relation

The Explicit Formula of the Presumed Optimal Recurrence Relation for the Star Tower of Hanoi