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 a vertex of degree 3b.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 a vertex of degree 3b.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
The correct answer is c. The graph must have a vertex of degree 4.
Here's why:
In a simple undirected graph, the degree of a vertex is the number of edges connected to it. The minimum degree in this graph is 2 and the maximum degree is 5. This means that every vertex in the graph has at least 2 edges and at most 5 edges connected to it.
a. The graph does not necessarily have to have a vertex of degree 3. It could be that all vertices have a degree of 2 or 5.
b. The graph cannot have a vertex of degree 6 because the maximum degree is stated to be 5.
d. The graph cannot have a vertex of degree 7 because the maximum degree is stated to be 5.
Therefore, the only statement that must be true is c. The graph must have a vertex of degree 4. This is because 4 is within the range of the minimum and maximum degree (2 and 5, respectively).
Similar Questions
Consider a simple undirected graph with 6 vertices. The degrees of the vertices in this graph are as follows: vertex A has degree 3, vertex B has degree 2, vertex C has degree 4, vertex D has degree 3, vertex E has degree 3, and vertex F has degree 1. Calculate the number of edges in the graph.a.6b.7c.8d.12
A graph has 6 vertices, and each vertex has a degree of 2 except for one vertex, which has a degree of 4. Determine the number of edges in the graph.a.4b.7c.12d.16
What is the degree of a vertex in a graph?a) Number of edges connected to the vertexb) Number of vertices in the graphc) Number of self-loopsd) Number of paths through the vertex
Which of the following values can be the degrees of an undirected graph with 7 vertices? Group of answer choices 3, 1, 4, 1, 5, 2, 5 5, 5, 5, 5, 5, 5, 5 2, 6, 2, 1, 4, 4, 3 4, 3, 2, 3, 0, 6, 2
Which of the following sequences can not be the degree sequence of any graph when the degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order ?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1 OptionsII and IIIII and IVI and IIIII Only
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.