4.6.3: Inferring information about a graph from matrices of graph powers.

A directed graph G has 5 vertices, numbered 1 through 5. The 55 matrix A is the adjacency matrix for G. The matrices A2 and A3 are given below.

Use the information given to answer the questions about the graph G.

(a)

Which vertices can reach vertex 2 by a walk of length 3?

(b)

What is the out-degree of vertex 4 in the transitive closure of G?

(c)

Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A4 = A2A2.)

(d)

Is (2, 2) in the transitive closure of G?

(e)

Is (5, 3) an edge in G3?

(f)

Is there a circuit of length 3 in G?

00010 00001 00110 01011 10001 3 00001 00010 01001 10001 00110 2