The Structure of the Heawood Graph

TL;DR

This paper analyzes the cycle structure of the Heawood graph, detailing automorphism actions and enumerations of various cycles, enhancing understanding of its symmetry and combinatorial properties.

Contribution

It provides a detailed description of the cycle structure and automorphism group actions on the Heawood graph, including enumeration of specific cycles and cycle pairs.

Findings

Automorphism group acts transitively on 12-cycles, Hamiltonian cycles, and disjoint 6-cycle pairs.

Enumerates 12-, 10-, and 8-cycles in the Heawood graph.

Counts pairs of disjoint 6-cycles in the graph.

Abstract

We give a description of the cycle structure of the Heawood graph, $C_{14}$. In particular, we prove that the automorphism group of $C_{14}$ acts transitively on the set of $12$-cycles, Hamiltonian cycles, and disjoint pairs of $6$-cycles. We also enumerate $12$-, $10$-, and $8$-cycles in $C_{14}$, as well as pairs of disjoint $6$-cycles.