# Trees and Graphs : Vertices and Edges

1. True or False. It is possible to obtain a graph in which the number of vertices is 9, each with degree 5.

2. How many edges are there in a tree with 14 vertices? Choose one answer.

(a) 10 (b) 13 (c) 14 (d) 15 (e) none of the above

3. If there 5 sections of Discrete Math with a total enrollment of 31 students, what is the smallest possible number of students in the section with the largest enrollment?

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#### Solution Preview

1. True or False. It is possible to obtain a graph in which the number of vertices is 9, each with degree 5.

The answer is False, as there are no 5-regular graphs of order 9.

2. How many edges are there in a tree with 14 vertices? Choose one answer.

(a) 10 (b) 13 (c) 14 (d) 15 (e) none of ...

#### Solution Summary

Trees and Graphs, Vertices and Edges are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.