The Hanoi Graph H43

Metric properties of Hanoi graphs are not as well understood as those of the closely related, but structurally simpler Sierpiński graphs . The most outstanding open problem is to find the domination number of Hanoi graphs. Here we concentrate on the first non-trivial case of , which contains no 1-pe...

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Bibliographic Details
Published inDiscussiones Mathematicae. Graph Theory Vol. 40; no. 4; pp. 1095 - 1109
Main Authors Hinz, Andreas M., Movarraei, Nazanin
Format Journal Article
LanguageEnglish
Published Sciendo 01.11.2020
University of Zielona Góra
Subjects
05C12
05C15
05C69
domination number
dominator chromatic number
Hanoi graphs
metric dimension
Sierpiński graphs
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Summary:Metric properties of Hanoi graphs are not as well understood as those of the closely related, but structurally simpler Sierpiński graphs . The most outstanding open problem is to find the domination number of Hanoi graphs. Here we concentrate on the first non-trivial case of , which contains no 1-perfect code. The metric dimension and the dominator chromatic number of will be determined as well. This leads to various conjectures for the general case and will thus provide an orientation for future research.
ISSN:2083-5892
DOI:10.7151/dmgt.2202