Characterisation of symmetries of unlabelled triangulations and its applications

TL;DR

This paper fully characterizes the symmetries of unlabelled triangulations and uses these insights to enumerate unlabelled cubic planar graphs, advancing understanding of their structural properties.

Contribution

It provides a complete symmetry classification and a constructive decomposition method for unlabelled triangulations, enabling enumeration of unlabelled cubic planar graphs.

Findings

Complete symmetry characterization of unlabelled triangulations

Constructive decomposition based on symmetries

Enumeration formulas for unlabelled cubic planar graphs

Abstract

We give a full characterisation of the symmetries of unlabelled triangulations and derive a constructive decomposition of unlabelled triangulations depending on their symmetries. As an application of these results we can deduce a complete enumerative description of unlabelled cubic planar graphs.