Is there a graph on 6 vertices with degrees 2, 3, 4, 5, 6, 7?

Question 1Select one:

False


True

The statement is **False**.

Here’s why: In any graph, the degree of a vertex cannot exceed the number of vertices minus 1, because a vertex can only connect to at most \( n - 1 \) other vertices in a graph with \( n \) vertices.

In this case, you have 6 vertices. The highest possible degree for any vertex in a graph with 6 vertices is 5 (since it can be connected to the other 5 vertices). However, one of the specified degrees is 7, which is not possible because there aren’t enough vertices for a vertex to have 7 connections in a 6-vertex graph.

Would you like more details or have any questions? Here are some related questions:

1. What is the degree sequence in graph theory?
2. Can there be a graph where all vertices have the same degree?
3. What is the sum of degrees of all vertices in a graph with 6 vertices?
4. What is the maximum degree in a complete graph with \(n\) vertices?
5. How do we check if a given degree sequence is graphical?

**Tip:** In any graph with \( n \) vertices, the sum of all degrees is always even due to the handshaking lemma.

Is there a graph on 6 vertices with degrees 2, 3, 4, 5, 6, 7?

Explore the limitations of vertex degrees in a graph with 6 vertices. Learn why it is impossible for a vertex to have a degree of 7 in such a graph due to the handshaking lemma and maximum degree rule. Suitable for high school students studying graph theory.

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