Geodesic
The Hanoi Graph $H_4^3$
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1095-1109

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Metric properties of Hanoi graphs H_p^n are not as well understood as those of the closely related, but structurally simpler Sierpiński graphs S_p^p. The most outstanding open problem is to find the domination number of Hanoi graphs. Here we concentrate on the first non-trivial case of H_4^3, which contains no 1-perfect code. The metric dimension and the dominator chromatic number of H_4^3 will be determined as well. This leads to various conjectures for the general case and will thus provide an orientation for future research.
Keywords: Hanoi graphs, Sierpiński graphs, metric dimension, domination number, dominator chromatic number 
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Hinz, Andreas M.; Movarraei, Nazanin. The Hanoi Graph $H_4^3$. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1095-1109. http://geodesic.mathdoc.fr/item/DMGT_2020_40_4_a10/