Chapter 11.2, Problem 14E

Consider the digraphs $G_1$, $G_2$ shown.

1. Find the adjacency matrix $A_1$ of $G_1$ and the adjacency matrix $A_2$ of $G_2$.

2. Explain why the map $\phi :G_1\to G_2$ defined by

   $\begin{array}{l}\phi (v_1)=u_1,\phi {\text{(v}}_2{\text{)= u}}_1\\ \phi (v_3)=u_4,\phi {\text{(v}}_4{\text{)= u}}_3\end{array}$

3. Find the permutation matrix P that corresponds to $\phi$ and satisfies. $P{A}_1{P}^T=A_2$.

4. Are these digraphs strongly connected?

5. Are these digraphs Eulerian?