Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(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.

(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.

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
### Problem Statement (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. ### Graphs Description - **Graph on the Left:** - Vertices: A, B, C, D, E - Edges: A-B, B-C, C-D, D-E, E-A - Structure: This is a pentagon, showing a cyclic structure with 5 vertices connected in a closed loop. - **Graph on the Right:** - Vertices: a, b, c, d, e - Edges: a-b, b-c, c-d, d-a, a-e - Structure: This graph also shows a pentagon. However, vertex 'a' has an additional edge connecting it to vertex 'e', forming a different connectivity structure and having one vertex of higher degree than others. ### Explanation The task is to demonstrate that these two graphs are not isomorphic by identifying a property that is preserved under isomorphism but differs between the two graphs. An immediately apparent difference is that the degrees of the vertices in each graph differ. In the left graph, all vertices have the same degree, while in the right graph, there is one vertex with a different degree, indicating they cannot be isomorphic.
Transcribed Image Text:### Problem Statement (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. ### Graphs Description - **Graph on the Left:** - Vertices: A, B, C, D, E - Edges: A-B, B-C, C-D, D-E, E-A - Structure: This is a pentagon, showing a cyclic structure with 5 vertices connected in a closed loop. - **Graph on the Right:** - Vertices: a, b, c, d, e - Edges: a-b, b-c, c-d, d-a, a-e - Structure: This graph also shows a pentagon. However, vertex 'a' has an additional edge connecting it to vertex 'e', forming a different connectivity structure and having one vertex of higher degree than others. ### Explanation The task is to demonstrate that these two graphs are not isomorphic by identifying a property that is preserved under isomorphism but differs between the two graphs. An immediately apparent difference is that the degrees of the vertices in each graph differ. In the left graph, all vertices have the same degree, while in the right graph, there is one vertex with a different degree, indicating they cannot be isomorphic.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 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