Checking for Graph Isomorphism

To verify their isomorphism, define the bijective function: $f(1) = A$, $f(2) = C$, $f(3) = B$, and $f(4) = D$.

Using this function, note how the following edges correspond:

• $\{1,2\} \Leftrightarrow \{A,C\}$
• $\{2,4\} \Leftrightarrow \{C,D\}$
• $\{1,3\} \Leftrightarrow \{A,B\}$
• $\{3,4\} \Leftrightarrow \{B,D\}$
• $\{4,1\} \Leftrightarrow \{D,A\}$

Since the structure is preserved, we have $G_1 \cong G_2$.