# Prove that the graphs $G$ and $H$ are not isomorphic

Let $$G$$ be the graph on the left and $$H$$ be the graph on the right.

For $$G$$:

number of edges: $$9$$

number of vertices: $$6$$

degree sequence: $$3,3,3,3,3,3$$

For $$H$$:

number of edges: $$9$$

number of vertices: $$6$$

degree sequence: $$3,3,3,3,3,3$$

I am having trouble proving these two are not isomorphic. I see $$4$$-cycles in $$H$$ but not in $$G$$.

• Please exhibit a cycle of odd length in $H$. There are none. Dec 12 '18 at 16:47
• Was a reply to someone else's comment that they have since deleted. See my answer below. Dec 12 '18 at 17:14