A planar graph can have 7 vertices, 9 edges, and 3 faces.Question 2Select one:TrueFalse

1. Break Down the Problem

To determine whether a planar graph can have 7 vertices, 9 edges, and 3 faces, we will apply Euler's formula for planar graphs, which states: $V - E + F = 2$ where $V$ is the number of vertices, $E$ is the number of edges, and $F$ is the number of faces.

2. Relevant Concepts

From the problem, we have:

• $V = 7$ (vertices)
• $E = 9$ (edges)
• $F = 3$ (faces)

3. Analysis and Detail

Substituting the values into Euler’s formula: $7 - 9 + 3 = 2$

Calculating the left side: $7 - 9 + 3 = 1$ This does not equal 2; hence, the values do not satisfy Euler’s formula for planar graphs.

4. Verify and Summarize

Since the calculation does not satisfy Euler's formula, we conclude that it is not possible for a planar graph to have 7 vertices, 9 edges, and 3 faces.

Final Answer

False. A planar graph cannot have 7 vertices, 9 edges, and 3 faces.