# G-degree for singular manifolds

## TL;DR

This paper investigates the G-degree of colored graphs representing singular manifolds, providing a complete topological classification up to G-degree 6 in three dimensions, advancing understanding in quantum gravity models.

## Contribution

It offers the first comprehensive classification of G-degree for singular manifold graphs in 3D, linking graph properties to topological features.

## Key findings

- Complete classification of G-degree up to 6 in 3D
- All 4-colored graphs in this class represent singular manifolds
- Establishes connections between G-degree and manifold topology

## Abstract

The G-degree of colored graphs is a key concept in the approach to Quantum Gravity via tensor models. The present paper studies the properties of the G-degree for the large class of graphs representing singular manifolds (including closed PL manifolds). In particular, the complete topological classification up to G-degree 6 is obtained in dimension 3, where all 4-colored graphs represent singular manifolds.