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Symmetry 2017, 9(11), 274; doi:10.3390/sym9110274

Operations on Oriented Maps

1
Department of Information Sciences and Technologies (FAMNIT), University of Primorska, 6000 Koper, Slovenia
2
Department of Mathematics & Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775, USA
*
Author to whom correspondence should be addressed.
Received: 31 July 2017 / Revised: 7 November 2017 / Accepted: 11 November 2017 / Published: 14 November 2017
(This article belongs to the Special Issue Polyhedral Structures)
View Full-Text   |   Download PDF [446 KB, uploaded 15 November 2017]   |  

Abstract

A map on a closed surface is a two-cell embedding of a finite connected graph. Maps on surfaces are conveniently described by certain trivalent graphs, known as flag graphs. Flag graphs themselves may be considered as maps embedded in the same surface as the original graph. The flag graph is the underlying graph of the dual of the barycentric subdivision of the original map. Certain operations on maps can be defined by appropriate operations on flag graphs. Orientable surfaces may be given consistent orientations, and oriented maps can be described by a generating pair consisting of a permutation and an involution on the set of arcs (or darts) defining a partially directed arc graph. In this paper we describe how certain operations on maps can be described directly on oriented maps via arc graphs. View Full-Text
Keywords: map; oriented map; truncation; dual; medial; snub; flag graph; arc graph map; oriented map; truncation; dual; medial; snub; flag graph; arc graph
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Pisanski, T.; Williams, G.; Berman, L.W. Operations on Oriented Maps. Symmetry 2017, 9, 274.

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