The Hanoi Graph H43

Metric properties of Hanoi graphs Hnp are not as well understood as those of the closely related, but structurally simpler Sierpiński graphs Snp. The most outstanding open problem is to find the domination number of Hanoi graphs. Here we concentrate on the first non-trivial case of H34, which contains no 1-perfect code. The metric dimension and the dominator chromatic number of H34 will be determined as well. This leads to various conjectures for the general case and will thus provide an orientation for future research