# What is NAP?

NAP stands for No Automorphisms, Please!
The goal is to add edges and nodes to the graph to break all symmetries. The fewer added edges and nodes, the better! There's a new puzzle every day.

## What counts as a symmetry?

In this case, a symmetry is any 'relabeling' of the nodes that maintains the structure of the graph. If we take some node, we can call the set of all nodes connected to it via some edge its neighbors. Then a symmetry of a graph shuffles some nodes around, but makes sure each node has the same neighbors. Such a symmetry is called an automorphism.
For example, we can label the following graph and its one symmetry. Sometimes, the automorphisms look like the standard symmetry we're used to—reflections and rotations—like how the one above looks like a reflection. But often it can be more subtle and not look like any geometric symmetry. For example, the following is an automorphism that doesn't conform to our standard notion of reflection or rotation:
Note that the actual physical movement of the graph doesn't affect its symmetries, so the following two graphs are the same:
so they have the same symmetries.
This is an example of a graph with no automorphisms (a winning graph!):

## Manipulating the graph

Click the Edit button, then click Add Node and click anywhere near the graph to add a node. To add an edge, click Add Edge, then drag click your cursor from one node to another. When you think you have a graph with no symmetries, click Check Symmetries! You get 1 point for each edge added and 2 points for each node added. Your goal is to minimize your score.
If a node leaves the screen by accident, you can zoom out (or in) with the navigation buttons.