Crossing numbers of Sierpiński‐like graphs

The crossing number of Sierpiński graphs S(n, k) and their regularizations S(n, k) and S(n, k) is studied. Explicit drawings of these graphs are presented and proved to be optimal for S(n, k) and S(n, k) for every n ≥ 1 and k ≥ 1. These are the first nontrivial families of graphs of “fractal” type whose crossing number is known.

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