Medial symmetry type graphs
type: Item
instance of: scholarly article
title: Medial symmetry type graphs
zbMATH Open document ID: 1301.05170
author: Isabel Hubard
author: María Del Río Francos
author: Alen Orbanić
author: Tomaž Pisanski
published in: The Electronic Journal of Combinatorics
publication date: 2014-08-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1301.7637
full work available at URL: v20i3p29
review text: Summary: A \(k\)-orbit map is a map with its automorphism group partitioning the set of flags into \(k\) orbits. Recently \(k\)-orbit maps were studied by \textit{A. Orbanić} et al. [J. Comb. Theory, Ser. A 117, No. 4, 411--429 (2010; Zbl 1197.51005)], for \(k \leq 4\). In this paper we use symmetry type graphs to extend such study and classify all the types of 5-orbit maps, as well as all self-dual, properly and improperly, symmetry type of \(k\)-orbit maps with \(k\leq 7\). Moreover, we determine, for small values of \(k\), all types of \(k\)-orbits maps that are medial maps. Self-dualities constitute an important tool in this quest.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 52B15
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 6330301
zbMATH Keywords: symmetry type graph
zbMATH Keywords: medial map
zbMATH Keywords: \(k\)-orbit map
zbMATH Keywords: flag graph
MaRDI profile type: Publication
arXiv ID: 1301.7637
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description: scientific article; zbMATH DE number 6330301