Q11. Let T be a spanning tree of graph G. Suppose the spanning tree T has 13 edges. How many vertices must there be in the graph G? Your Answer: Answer
Q11. Let T be a spanning tree of graph G. Suppose the spanning tree T has 13 edges. How many vertices must there be in the graph G? Your Answer: Answer
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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![**Question 11:** Let \( T \) be a spanning tree of graph \( G \). Suppose the spanning tree \( T \) has 13 edges. How many vertices must there be in the graph \( G \)?
**Your Answer:**
[Text Box for Input]
**Answer:**
In a spanning tree, the number of edges is always one less than the number of vertices. Therefore, if the spanning tree \( T \) has 13 edges, the number of vertices in \( G \) must be:
\[ V = E + 1 = 13 + 1 = 14 \]
So, the graph \( G \) must have 14 vertices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc6fbff9-4759-45b9-9f61-27046377aa96%2F86af6d7a-5539-46d6-839d-183814c3aac6%2Frub1gem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 11:** Let \( T \) be a spanning tree of graph \( G \). Suppose the spanning tree \( T \) has 13 edges. How many vertices must there be in the graph \( G \)?
**Your Answer:**
[Text Box for Input]
**Answer:**
In a spanning tree, the number of edges is always one less than the number of vertices. Therefore, if the spanning tree \( T \) has 13 edges, the number of vertices in \( G \) must be:
\[ V = E + 1 = 13 + 1 = 14 \]
So, the graph \( G \) must have 14 vertices.
Transcribed Image Text:**Q12B. Assess whether the statement is true or false:**
The graph shown is a tree.
**Diagram Explanation:**
The diagram is a graph with the following vertices labeled: a, b, c, d, e, f, and g. These vertices are connected by edges, forming a complex structure with multiple connections and cycles.
- Vertex a connects to vertices b, f, and g.
- Vertex b connects to vertices a, c, and f.
- Vertex c connects to vertices b, d, and f.
- Vertex d connects to vertices c and e.
- Vertex e connects to vertex d.
- Vertex f connects to vertices a, b, c, and g.
- Vertex g connects to vertices a and f.
This graph contains cycles, which are sequences of edges and vertices wherein a vertex is reachable from itself.
**Question:**
☐ True
☐ False
In determining whether the graph is a tree, consider that a tree is an acyclic connected graph with exactly one path connecting any two vertices. In this case, the presence of cycles indicates the graph is not a tree.
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