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; in 1992, Archdeacon and Richter described a method for constructing all self-dual plane graphs and a second construction was produced by Servatius and Christopher 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.
@article{10_37236_3510,
author = {Jack E. Graver and Elizabeth J. Hartung},
title = {Self-dual spherical grids},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/3510},
zbl = {1300.05077},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3510/}
}
TY - JOUR
AU - Jack E. Graver
AU - Elizabeth J. Hartung
TI - Self-dual spherical grids
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/3510/
DO - 10.37236/3510
ID - 10_37236_3510
ER -
%0 Journal Article
%A Jack E. Graver
%A Elizabeth J. Hartung
%T Self-dual spherical grids
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3510/
%R 10.37236/3510
%F 10_37236_3510
Jack E. Graver; Elizabeth J. Hartung. Self-dual spherical grids. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3510
