Self-dual spherical grids

Jack E. Graver, Elizabeth J. Hartung

Research output: Contribution to journalArticle

Abstract

Self-dual plane graphs have been studied extensively. C. A. B Smith and W. T. Tutte published A class of self-dual maps in 1950 [9]; in 1992, Archdeacon and Richter [1] described a method for constructing all self-dual plane graphs and a second construction was produced by Servatius and Christopher [5] in 1992. Both constructions are inductive. In this paper, we produce four templates from which all self-dual plane graphs with maximum degree 4 (self-dual spherical grids) can be constructed. The self-dual spherical grids are further subdivided into 27 basic automorphism classes. Self-dual spherical grids in the same automorphism class have similar architecture. A smallest example of each class is constructed.

Original languageEnglish (US)
JournalElectronic Journal of Combinatorics
Volume21
Issue number1
DOIs
StatePublished - Feb 21 2014

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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