If two graphs are isomorphic, which of the follow must be true? They have the same number of vertices and edges They have the same degree sequences They have the same labels They list their vertices in the same order
If two graphs are isomorphic, which of the follow must be true? They have the same number of vertices and edges They have the same degree sequences They have the same labels They list their vertices in the same order
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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Discrete Math
![**Question on Graph Isomorphism:**
If two graphs are isomorphic, which of the following must be true?
- [ ] They have the same number of vertices and edges
- [ ] They have the same degree sequences
- [ ] They have the same labels
- [ ] They list their vertices in the same order
Note: Understanding whether two graphs are isomorphic involves identifying if there is a one-to-one correspondence between their vertex sets that preserves the edge connectivity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34cc5c6b-5450-4c98-93f3-d37eba173724%2F3bcbead6-d0f5-45be-aa99-70a420c5fe41%2Fsykyyzm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question on Graph Isomorphism:**
If two graphs are isomorphic, which of the following must be true?
- [ ] They have the same number of vertices and edges
- [ ] They have the same degree sequences
- [ ] They have the same labels
- [ ] They list their vertices in the same order
Note: Understanding whether two graphs are isomorphic involves identifying if there is a one-to-one correspondence between their vertex sets that preserves the edge connectivity.
Expert Solution
Step 1: Introduction
We know that
The isomorphism of a graph can be described as a graph in which a single graph can have more than one form.
That is two different graphs can have the same number of edges, vertices, and same edges connectivity. These types of graphs are known as isomorphic graphs.
An unlabelled graphs can also be an isomorphic graphs .
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