Abstract
The median of a graph consists of those vertices which minimize the average distance to all other vertices. It plays an important role in optimization scenarios like facility location problems. Sierpiński graphs are the state graphs of the Switching Tower of Hanoi problem, a variant of the Tower of Hanoi game. They also provide optimum models for interconnection networks. In this study, we present our observations on the median of Sierpiński graphs. We conjecture that the number of median vertices in S 3 n is always 12, if n ≥ 3 , and that they lie around the inner ring of the standard drawing.
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