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A directed graph G has 5 vertices, numbered 1 through 5. The 5x5 matrix A is the adjacency matrix for G. The matrices A? and A³ are given below. 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 10 0 0 1 0 0 1 0 0 1 A? = 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1

A directed graph G has 5 vertices, numbered 1 through 5. The 5x5 matrix A is the adjacency matrix for G. The matrices A? and A³ are given below. 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 10 0 0 1 0 0 1 0 0 1 A? = 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

(a)

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

(d)

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

(e)

Is (5, 3) an edge in G3?

(f)

Is there a closed walk of length 3 in G?

A directed graph G has 5 vertices, numbered 1 through 5. The 5x5 matrix A is the adjacency matrix for G. The matrices A? and A3 are given below. 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 A? 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 10
Transcribed Image Text:A directed graph G has 5 vertices, numbered 1 through 5. The 5x5 matrix A is the adjacency matrix for G. The matrices A? and A3 are given below. 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 A? 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 10
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