# Orbital Graphs

## TL;DR

This paper introduces orbital graphs, explores their fundamental properties, and demonstrates their usefulness in improving search algorithms for permutation groups, such as group intersection and stabilizer computations.

## Contribution

It presents the concept of orbital graphs and applies them to enhance algorithms for permutation group problems.

## Key findings

- Orbital graphs have useful properties for group search algorithms.
- They improve efficiency in finding group intersections.
- They assist in computing stabilizers of sets within groups.

## Abstract

We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.