Chapter 10.3, Problem 6E

(a)

To determine

To Prove: The number of walks of length 2 in G is the sum of the entries of the matrix $A^2$.

(b)

To determine

To prove: Let $d_i$ denote the degree of the vertex $v_i$ in G. Show that the sum of the entries of $A^2$ is also ${\displaystyle \sum d_1^2}$