Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
List all the isomorphisms between the two graphs given in Figure 12.23. Explain why there are no others. 3 5 √2 6 + e b f d Figure 12.23 Graphs with several isomorphisms

List all the isomorphisms between the two graphs given in Figure 12.23. Explain why there are no others. 3 5 √2 6 + e b f d Figure 12.23 Graphs with several isomorphisms

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

Discrete Math

**Educational Explanation** The image contains a task that involves determining isomorphisms between two graphs illustrated in Figure 12.23. The instruction given is: "List all the isomorphisms between the two graphs given in Figure 12.23. Explain why there are no others." **Graphs Description:** - **Left Graph:** - This graph is a pentagon with one vertex on top, labeled as "1." - The rest of the vertices are labeled "2," "3," "4," "5," and "6." - The edges consist of: (1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (5, 6), and (4, 6). - **Right Graph:** - This graph mirrors the structure of the left graph and is similarly a pentagon with one vertex on top, labeled as "a." - The remaining vertices are labeled "b," "c," "d," "e," and "f." - Corresponding edges are: (a, b), (a, c), (b, c), (b, d), (c, e), (e, f), and (d, f). **Concept Explanation:** An isomorphism between graphs is a one-to-one mapping between the vertex sets of the graphs such that the adjacency of vertices is preserved. The task asks for all such mappings between the vertices of the two graphs where the edges (connections) remain the same. **Analysis:** - **Isomorphic Mapping Example:** - Vertex "1" could be mapped to "a." - Vertices "2," "3," "4," "5," "6" could be mapped respectively to "b," "c," "d," "e," "f" due to the preserved adjacency relationships. The analysis involves finding all such possible mappings and verifying that they preserve the structure of adjacency uniquely compared to any other combinations, hence exploring the uniqueness of isomorphisms.
Transcribed Image Text:**Educational Explanation** The image contains a task that involves determining isomorphisms between two graphs illustrated in Figure 12.23. The instruction given is: "List all the isomorphisms between the two graphs given in Figure 12.23. Explain why there are no others." **Graphs Description:** - **Left Graph:** - This graph is a pentagon with one vertex on top, labeled as "1." - The rest of the vertices are labeled "2," "3," "4," "5," and "6." - The edges consist of: (1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (5, 6), and (4, 6). - **Right Graph:** - This graph mirrors the structure of the left graph and is similarly a pentagon with one vertex on top, labeled as "a." - The remaining vertices are labeled "b," "c," "d," "e," and "f." - Corresponding edges are: (a, b), (a, c), (b, c), (b, d), (c, e), (e, f), and (d, f). **Concept Explanation:** An isomorphism between graphs is a one-to-one mapping between the vertex sets of the graphs such that the adjacency of vertices is preserved. The task asks for all such mappings between the vertices of the two graphs where the edges (connections) remain the same. **Analysis:** - **Isomorphic Mapping Example:** - Vertex "1" could be mapped to "a." - Vertices "2," "3," "4," "5," "6" could be mapped respectively to "b," "c," "d," "e," "f" due to the preserved adjacency relationships. The analysis involves finding all such possible mappings and verifying that they preserve the structure of adjacency uniquely compared to any other combinations, hence exploring the uniqueness of isomorphisms.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
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