Mathematical analysis reveals identical discrete fractal dimensions across Sierpinski and Hanoi graphs, confirming the structural role of quasi-isometric invariance.
This paper studies several fractal dimensions of the Sierpinski skeleton graph, an infinite planar graph. By building explicit quasi-isometries between the Sierpinski skeleton graph, the integer Sierpinski graph and the Hanoi graph, we prove that these three graphs share the same values of lower, Hausdorff, packing, and mass dimensions, all equal to log 3/ log 2. The proof relies on the quasi-isometric invariance of these discrete fractal dimensions, established in a companion paper.
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Xie et al. (2026) studied this question.
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