**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. **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 ☐ FalseIn 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.

To find the number of vertices of a tree has 13 edges of its spanning tree.

Answered: Q11. Let T be a spanning tree of graph…

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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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