Checking for Graph Isomorphism

4. Different Number of Connected Components.
   Example: One graph is built of a single connected component (all verices are reachable from each other) and the other has 2 connected components (at least one vertex can't be reached from another vertex).
5. Different Number of Self-Loops.
   Example: In graph \(G_1\), $3$ vertices have loops, while in \(G_2\), only $2$ vertices have loops.
6. Different Cycle Structures.
   Example: $G_1$ has a $5$-vertex loop, while $G_2$ has only $4$-vertex loops or shorter than $4$-vertex.

---

Since isomorphic graphs are ones in which the vertices were re-arranged in space (without vertices, edges, or structure being deleted or modified,) we can demonstrate how to 'shift' one graph into another by moving its vertices.

One convenient online app for constructing graphs and beign able to move them in space is Graph Editor by CS Academy.
Feel free to use it when working with graphs!