a. Is it possible to have six vertices of degrees 1, 1, 2, 2, 2, and...

Question

Question

a. Is it possible to have six vertices of degrees 1, 1, 2, 2, 2, and 3? If not, explain why?

b. Explain why you cannot have a full binary tree with 16 vertices of which 6 are internal vertices.

engineering Computer-Science

Answer 1

Answer #1

Answer:

a)

Answer 2

Similar Homework Help Questions

1. If T is a tree with 999 vertices, then T has_edges (5 pts) 2. There...

1. If T is a tree with 999 vertices, then T has_edges (5 pts) 2. There are 3. The best comparison-based sorting algorithms for a list of n items have complexity ). (5 pts) 4. If T is a binary tree with 100 vertices, its minimum height is 5. If T is a full binary tree with 101 vertices, its maximum height is 6. If T is a full binary tree with 50 leaves, its minimum height is 7. Every...
6. (a) Decide if there exists a full binary tree with twelve vertices. If so, draw...

6. (a) Decide if there exists a full binary tree with twelve vertices. If so, draw the tree. If not explain why not. (b) Let G be a finite simple undirected graph in which each vertex has degree at least 2. Prove that G must contain a simple circuit (c) Let G be a graph with 2 vertices of degree 1, 3 of degree 2, and 2 of degree 3. Prove that G cannot be a tree
Exercise 1 (a) Proof that (by an example with10) the number of terminal vertices in a...

Exercise 1 (a) Proof that (by an example with10) the number of terminal vertices in a binary tree with n vertices is (n 1)/2. (b) Give an example of a tree (n> 10) for which the diameter is not equal to the twice the radius. Find eccentricity, radius, diameter and center of the tree. (c) If a tree T has four vertices of degree 2, one vertex of degree 3, two vertices of degree 4, and one vertex of degree...

suppose that a full 4-ary tree has 100 leaves. howmany internal vertices does it have? please...

suppose that a full 4-ary tree has 100 leaves. howmany internal vertices does it have? please explain in detail. i dont want to know about no. of vertices i just need to find internal vertices . can you also explain how is 4 ary tree look alike.? thanks,
Let G be a tree with v vertices which has precisely four vertices of degree 1 and precisely two vertices of degree 3. What are the degrees of the remaining vertices? Let G be a tree with v verti...

Let G be a tree with v vertices which has precisely four vertices of degree 1 and precisely two vertices of degree 3. What are the degrees of the remaining vertices? Let G be a tree with v vertices which has precisely four vertices of degree 1 and precisely two vertices of degree 3. What are the degrees of the remaining vertices?
Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five...

Answer each question in the space provided below. 1. Draw all non-isomorphic free trees with five vertices. You should not include two trees that are isomorphic. 2. If a tree has n vertices, what is the maximum possible number of leaves? (Your answer should be an expression depending on the variable n. 3. Find a graph with the given set of properties or explain why no such graph can exist. The graphs do not need to be trees unless explicitly...

Suppose that a full m-ary tree T has 109 vertices and height 2. (a) What are the possible values of m? (b) Assume also that T has at least 84 leaves. Now what are the possible values of m? (c) What v...

Suppose that a full m-ary tree T has 109 vertices and height 2. (a) What are the possible values of m? (b) Assume also that T has at least 84 leaves. Now what are the possible values of m? (c) What value of m maximizes the number of internal vertices in T? (d) For this value of m identify the number of leaves and number of internal vertices at each level of T.
Suppose that a full m-ary tree T has 109 vertices and height 2. (a) What are...

Suppose that a full m-ary tree T has 109 vertices and height 2. (a) What are the possible values of m? (b) Assume also that T has at least 84 leaves. Now what are the possible values of m? (c) What value of m maximizes the number of internal vertices in T? (d) For this value of m identify the number of leaves and number of internal vertices at each level of T.
Question 3. Draw a graph G = (V. E) on 10 nodes (vertices) with degrees 1.1.1.1.1.1.1.1.5,...

Question 3. Draw a graph G = (V. E) on 10 nodes (vertices) with degrees 1.1.1.1.1.1.1.1.5, 5. V = {0, V2.03......}. Is G a tree? Why/why not? (Remember that a tree is a graph which is connected and has no cycles).

Sketch a tree T with 10 vertices where 4 vertices have degree 3 and 6 vertices have degree 1.

Sketch a tree T with 10 vertices where 4 vertices have degree 3 and 6 vertices have degree 1.