Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(c) Prove that the two graphs below are isomorphic.

(c) Prove that the two graphs below are isomorphic.

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
Question
### (c) Prove that the two graphs below are isomorphic. #### Figure 4 Explanation: - **Description**: Two undirected graphs, each with 6 vertices. - **Arrangement and Vertices**: - **First Graph**: - Vertices are arranged in two rows and three columns. - Top row, from left to right: Vertices 1, 2, 3. - Bottom row, from left to right: Vertices 6, 5, 4. - Edges connect the following vertex pairs: (1,2), (2,3), (1,5), (2,5), (5,3), (2,4), (3,6), (6,4), (5,4). - **Second Graph**: - Vertices labeled a through f. - Vertices d, a, c (vertically inline). - Vertices e, f, b (horizontally to the right of vertices d, a, c, respectively). - Edges connect the following vertex pairs: (a,d), (a,c), (c,e), (e,a), (b,d), (b,a), (f,e), (c,f), (b,f). ### (d) Show that the pair of graphs are not isomorphic by showing that there is a property that is preserved under isomorphism which one graph has and the other does not. #### Figure 5 Explanation: - **Description**: Two undirected graphs. - **First Graph**: - Pentagonal arrangement with 5 vertices. - Vertices labeled 1, 2, 3, 4, 5 (top vertex to bottom, clockwise). - Edges connect: (1,2), (2,3), (3,4), (4,5), (5,1). - **Second Graph**: - 4 vertices labeled a, b, c, d. - Vertices d, c (horizontally inline, d is left of c). - Vertex a above d and c. - Vertex b right of a but above other vertices. - Edges connect: (a,b), (b,c), (a,d), (c,d), (d,b).
Transcribed Image Text:### (c) Prove that the two graphs below are isomorphic. #### Figure 4 Explanation: - **Description**: Two undirected graphs, each with 6 vertices. - **Arrangement and Vertices**: - **First Graph**: - Vertices are arranged in two rows and three columns. - Top row, from left to right: Vertices 1, 2, 3. - Bottom row, from left to right: Vertices 6, 5, 4. - Edges connect the following vertex pairs: (1,2), (2,3), (1,5), (2,5), (5,3), (2,4), (3,6), (6,4), (5,4). - **Second Graph**: - Vertices labeled a through f. - Vertices d, a, c (vertically inline). - Vertices e, f, b (horizontally to the right of vertices d, a, c, respectively). - Edges connect the following vertex pairs: (a,d), (a,c), (c,e), (e,a), (b,d), (b,a), (f,e), (c,f), (b,f). ### (d) Show that the pair of graphs are not isomorphic by showing that there is a property that is preserved under isomorphism which one graph has and the other does not. #### Figure 5 Explanation: - **Description**: Two undirected graphs. - **First Graph**: - Pentagonal arrangement with 5 vertices. - Vertices labeled 1, 2, 3, 4, 5 (top vertex to bottom, clockwise). - Edges connect: (1,2), (2,3), (3,4), (4,5), (5,1). - **Second Graph**: - 4 vertices labeled a, b, c, d. - Vertices d, c (horizontally inline, d is left of c). - Vertex a above d and c. - Vertex b right of a but above other vertices. - Edges connect: (a,b), (b,c), (a,d), (c,d), (d,b).
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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