Self-Dual Maps I: Antipodality

Self-dual maps on the sphere

We show how to recursively construct all self–dual maps on the sphere together with their self–dualities, and classify them according to their edge–permutations. Although several well known classes of self–dual graphs, e.g., the wheels, have been known since the last century, [7], the general characteristics of self–dual graphs have only recently begun to be explored. In [10] two constructions ...

Enumeration of self-dual planar maps

A planar map is an embedding of a connected planar graph in the sphere such that the surface is partitioned into simply connected regions; in other words, it is a finite cellular decomposition of the sphere into vertices, edges, and faces (0−, 1− and 2−cells, respectively). In particular, 3−connected planar maps correspond to polyhedra. Motivated by the Four Colour Problem, W. Tutte [4] launche...

Self { Dual Regular Maps from Medial Graphsd

Formally self-dual codes and Gray maps

In this paper we investigate binary formally self-dual codes as images of codes over rings using various Gray maps.

Harmonic Maps and Self - Dual Equations for Immersed Surfaces