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Hinz, Andreas M. and Movarraei, Nazanin (2020): THE HANOI GRAPH H-4(3). In: Discussiones Mathematicae Graph Theory, Vol. 40, 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 Sierpinski graphs S-p(n). 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.

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