# Graphs Problem 2

### Solution

The node e must match to itself, because it's the only node with degree 8. Similarly, the node a must match to itself because it's the only node with degree 3.

We then have two possible matches for node b: b or d. Once we've made this choice, the matches for d, g, and c are all forced by the need to preserve edge connections.

The ndes f, h, and k are all connected to the rest of the graph in the same way. So we can permute them freely when we do our match. So we have 3! choices for how to match these three nodes.

So in total, there are $$3! \cdot 2 = 12$$ isomorphisms from G to itself.