Planar Whitehead graphs with cyclic symmetry arising from the study of Dunwoody manifolds

James Howie, Gerald Williams

Research output: Contribution to journalArticle

Abstract

A fundamental theorem in the study of Dunwoody manifolds is a classification of finite graphs on 2n vertices that satisfy seven conditions (concerning planarity, regularity, and a cyclic automorphism of order n). Its significance is that if the presentation complex of a cyclic presentation is a spine of a 3-manifold then its Whitehead graph satisfies the first five conditions (the remaining conditions do not necessarily hold). In this paper we observe that this classification relies implicitly on an unstated 8th condition and that this condition is not necessary for such a presentation complex to be the spine of a 3-manifold. We expand the scope of Dunwoody’s classification by classifying all graphs that satisfy the first five conditions.
Original languageEnglish
Article number112096
JournalDiscrete Mathematics
Volume343
Issue number12
Early online date25 Aug 2020
DOIs
Publication statusE-pub ahead of print - 25 Aug 2020

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