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.