Chapter 10.3, Problem 10E

(a)

To determine

The adjacency matrices $A_1$ and $A_2$ of the graphs $G_1$ and $G_2$ shown.

(b)

To determine

The reason that the function $\phi :G_1\to G_2$ defined by

$\begin{array}{l}\phi (v_1)=u_4,\phi (v_2)=u_5,\phi (v_3)=u_1,\\ \phi (v_4)=u_3,\phi (v_5)=u_2\end{array}$

Is an isomorphism.

(c)

To determine

A permutation matrix P that corresponds to the isomorphism in (b) such that $P{A}_1{P}^T=A_2$.