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 contai...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2020-11-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2202 |
| _version_ | 1797757675036999680 |
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| author | Hinz Andreas M. Movarraei Nazanin |
| author_facet | Hinz Andreas M. Movarraei Nazanin |
| author_sort | Hinz Andreas M. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T18:19:01Z |
| format | Article |
| id | doaj.art-351bf41ff2e045f092e7a39f515b8eb9 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T18:19:01Z |
| publishDate | 2020-11-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-351bf41ff2e045f092e7a39f515b8eb92023-08-02T08:59:14ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922020-11-014041095110910.7151/dmgt.2202dmgt.2202The Hanoi Graph H43Hinz Andreas M.0Movarraei Nazanin1Department of Mathematics, Ludwig-Maximilians-Universität (LMU) München, 80333Munich, GermanyInternational Research Centre (IRC), Kalasalingam University, Tamil Nadu, IndiaMetric 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.https://doi.org/10.7151/dmgt.2202hanoi graphssierpiński graphsmetric dimensiondomination numberdominator chromatic number05c6905c1205c15 |
| spellingShingle | Hinz Andreas M. Movarraei Nazanin The Hanoi Graph H43 Discussiones Mathematicae Graph Theory hanoi graphs sierpiński graphs metric dimension domination number dominator chromatic number 05c69 05c12 05c15 |
| title | The Hanoi Graph H43 |
| title_full | The Hanoi Graph H43 |
| title_fullStr | The Hanoi Graph H43 |
| title_full_unstemmed | The Hanoi Graph H43 |
| title_short | The Hanoi Graph H43 |
| title_sort | hanoi graph h43 |
| topic | hanoi graphs sierpiński graphs metric dimension domination number dominator chromatic number 05c69 05c12 05c15 |
| url | https://doi.org/10.7151/dmgt.2202 |
| work_keys_str_mv | AT hinzandreasm thehanoigraphh43 AT movarraeinazanin thehanoigraphh43 AT hinzandreasm hanoigraphh43 AT movarraeinazanin hanoigraphh43 |