# Differential algebra of cubic planar graphs

## TL;DR

This paper introduces a combinatorial differential graded algebra associated with cubic planar graphs, linking algebraic structures to graph colorings and providing explicit computations and new insights into graph invariants.

## Contribution

It defines a novel combinatorial differential graded algebra for cubic planar graphs and connects its augmentation variety to graph colorings, offering new algebraic tools for graph theory.

## Key findings

- The algebra is explicitly constructed via counting binary sequences.
- The augmentation variety's rational points correspond to graph colorings.
- Explicit computations demonstrate the algebra's properties and applications.

## Abstract

In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In addition, in the appendix by K. Sackel the F(q)-rational points of its graded augmentation variety are shown to coincide with (q+1)-colorings of the dual graph.