Whether the graphs G and G' given below are isomorphic

Question

Whether the graphs G and G' given below are isomorphic?

Answer 1

As step 0, recall the notion of isomorphism of graphs. It is a trivial fact that if two graphs are isomorphic, then their connected components have the same number. But $G$ is not connected, but $G'$ is connected. Alternatively, find the minimal length of a cycle in $G$ resp. $G'$.

Answer 2

Any of the following is enough to show that $G\ncong G'$.

$1$.$K_3 \subseteq G$ while $K_3 \nsubseteq G'$

$2$. $G$ is disconeccted while $G'$ is connected

$3$. $P_4, P_5, P_6 \subseteq G'$ while $P_4, P_5, P_6 \nsubseteq G$