Abstract
Sierpiński graphs $S(n,3)$ are the graphs of the Tower of Hanoi puzzle with $n$ disks, while Sierpiński gasket graphs $S_n$ are the graphs naturally defined by the finite number of iterations that lead to the Sierpiński gasket. An explicit labeling of the vertices of $S_n$ is introduced. It is proved that $S_n$ is uniquely 3-colorable, that $S(n,3)$ is uniquely 3-edge-colorable, and that $\chi'(S_n)=4$, thus answering a question from~[15]. It is also shown that $S_n$ contains a 1-perfect code only for $n=1$ or $n=3$ and that every $S(n,3)$ contains a unique Hamiltonian cycle.
Citation
Sandi Klavˇzar. "COLORING SIERPIN´ SKI GRAPHS AND SIERPIN´ SKI GASKET GRAPHS." Taiwanese J. Math. 12 (2) 513 - 522, 2008. https://doi.org/10.11650/twjm/1500574171
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