In a simple undirected graph, the minimum degree is 2 and the maximum degree is 5. Which of the following statements is true?a.The graph must have vertices with degrees ranging from 2 to 5b.The graph must have a vertex of degree 6c.The graph must have a vertex of degree 4d.The graph must have a vertex of degree 7
Question
In a simple undirected graph, the minimum degree is 2 and the maximum degree is 5. Which of the following statements is true?a.The graph must have vertices with degrees ranging from 2 to 5b.The graph must have a vertex of degree 6c.The graph must have a vertex of degree 4d.The graph must have a vertex of degree 7
Solution 1
The correct answer is a. The graph must have vertices with degrees ranging from 2 to 5. This is because in a simple undirected graph, the degree of a vertex is the number of edges incident to it. Since the minimum degree is 2 and the maximum degree is 5, it means that there must be vertices with degrees that range from 2 to 5. The other options are incorrect because they mention degrees that are outside the given range (2 to 5).
Solution 2
To determine which statement is true, let's analyze the given information. We know that the minimum degree in the graph is 2 and the maximum degree is 5.
Statement a: "The graph must have vertices with degrees ranging from 2 to 5." This statement is true because the minimum degree is 2 and the maximum degree is 5, so all vertices in the graph must have degrees within this range.
Statement b: "The graph must have a vertex of degree 6." This statement is false because the maximum degree in the graph is 5, so there cannot be a vertex with a degree of 6.
Statement c: "The graph must have a vertex of degree 4." This statement is false because there is no specific requirement for a vertex to have a degree of 4. The degrees can range from 2 to 5.
Statement d: "The graph must have a vertex of degree 7." This statement is false because the maximum degree in the graph is 5, so there cannot be a vertex with a degree of 7.
Therefore, the correct statement is a: "The graph must have vertices with degrees ranging from 2 to 5."
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