Isomorphic Graphs
The two graphs above are isomorphic, which means that there exists an edge-preserving bijection from the set of vertices of the graph on the left to the set of vertices of the graph on the right.
How many such bijections are there?
We may first map \(u_1\) to any of the 5 vertices of the graph on the right (let's call this vertex \(v_1 \)). We then map \(u_2\) to either of \(v_1 \)'s 2 neighbors. The remaining vertices are then uniquely determined.