Recall that the adjacency matrix A for a graph has a 1 as the row i column j entry if there is an edge from the node vi to the node vj , and a 0 else. Further recall, for all positive integers k, that Ak ij gives the number of paths of length k from vi to vj . Consider the following graph:

Do the following: (a) Construct the adjacency matrix and enter it as a matrix A in Matlab.

(b) Use Matlab to find the matrix for the paths of length 2.

(c) Use Matlab to find the matrix for the paths of length 3.

(d) Use Matlab to find the matrix for the paths of length at most 3.

Your answer should be a Matlab diary or script showing the matrix A, and for each part (b) to (d) what Matlab statement or statements you used to find the answer, and Matlabs reply to each statement. Note that if you turn in a script, you also need to turn in Matlabs output for when you run that script.

V3 V2 U3 1)2 V1 V6 V3 'U4 1)4