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A graph has 25 vertices. How many edges are required for the graph to be a tree?Question 1Answera.24b.26c.19d.25

Question

A graph has 25 vertices. How many edges are required for the graph to be a tree?

Question 1
Answer

  • a. 24
  • b. 26
  • c. 19
  • d. 25
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Solution

Break Down the Problem

  1. Understand the definition of a tree: A tree is a connected graph with no cycles.
  2. Identify the relationship between vertices and edges in a tree.

Relevant Concepts

  1. A fundamental property of trees is that the number of edges E E in a tree with V V vertices is given by the formula:
    E=V−1 E = V - 1

Analysis and Detail

  1. Given that the number of vertices V=25 V = 25 : E=25−1=24 E = 25 - 1 = 24

Verify and Summarize

  • The calculations confirm that for a tree with 25 vertices, the number of edges should indeed be 24.

Final Answer

The required number of edges for the graph to be a tree is 24 (Option a).

This problem has been solved

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