Chapter 10, Problem 16RE

(a)

To determine

The adjacency matrix A of G.

(b)

To determine

The (1,5) entries of $A^2,A^3,A^4$ and $A^5$.

(c)

To determine

The an isomorphism $\phi :G\to H,$, where H is the graph on the right.

(d)

To determine

A permutation matrix P such that $PA{P}^T=B$. Check your answer by writing down B and computing the product $PA{P}^T$. If B is the adjacency matrix of H.