Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The edges between the vertices are represented by arrows, as follows: 4 to 3; 3 to 2; 2 to 1; I to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on vertex 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 × 5 matrix A is the adjacency matrix for G. The matrices A? and A are given below. 0 1 0 0 0 O 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 10 1 1 0 0 0 0 O o 1 0 0 O 0 0 0 10 0 0 1 10 1 1 1 0 10 A² = A³ = 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) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A= A² A²)

PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The edges between the vertices are represented by arrows, as follows: 4 to 3; 3 to 2; 2 to 1; I to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on vertex 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 × 5 matrix A is the adjacency matrix for G. The matrices A? and A are given below. 0 1 0 0 0 O 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 10 1 1 0 0 0 0 O o 1 0 0 O 0 0 0 10 0 0 1 10 1 1 1 0 10 A² = A³ = 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) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A= A² A²)

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
See similar textbooks
icon
Related questions
Topic Video
Question

See attached, answer part 2

PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: (2 3 6 Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The edges between the vertices are represented by arrows, as follows: 4 to 3; 3 to 2; 2 to 1; I to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on vertex 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 × 5 matrix A is the adjacency matrix for G. The matrices A² and A³ are given below. 0 1 0 0 0 O 0 0 10 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 A² = 1. 1 0 0 0 0 1 0 0 0 0 0 0 10 0 0 1 10 1 1 0 1 0 A3 = 1 Use the information given to answer the questions about the graph (a) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A4= A? A?.)
Transcribed Image Text:PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: (2 3 6 Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The edges between the vertices are represented by arrows, as follows: 4 to 3; 3 to 2; 2 to 1; I to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on vertex 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 × 5 matrix A is the adjacency matrix for G. The matrices A² and A³ are given below. 0 1 0 0 0 O 0 0 10 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 A² = 1. 1 0 0 0 0 1 0 0 0 0 0 0 10 0 0 1 10 1 1 0 1 0 A3 = 1 Use the information given to answer the questions about the graph (a) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A4= A? A?.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS