# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

A.M. Hinz, N. Movarraei

Title:

The Hanoi graph $H^{3}_{4}$

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-03-09, Revised: 2018-12-10, Accepted: 2018-12-10, https://doi.org/10.7151/dmgt.2202

Abstract:

Metric properties of Hanoi graphs $H_p^n$ are not as well understood as those of the closely related, but structurally simpler Sierpiński graphs $S_p^n$. 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.

Keywords:

Hanoi graphs, Sierpiński graphs, metric dimension, domination number, dominator chromatic number