Question 1: Check all that apply.

Consider the graph G (V,E) where V is the set of vertices and E is the set of undirected edges. V = {A, B, C, D, E} and E = {(D,C), (D,B), (E,B), (A,D)}.

If this graph is a tree and rooted at vertex B, then the subtree rooted at D includes these nodes. (It would help to draw the graph to answer the questions).

a. A

b. B

c. None of these answers

d. D

e. C

f. E

Question 2: Check all that apply.

Consider the graph G (V,E) where V is the set of vertices and E is the set of undirected edges. V = {A, B, C, D, E} and E = {(D,C), (E,C), (E,B), (A,D)}.

If this graph is a tree and rooted at vertex E, then these nodes are leaves. (It would help to draw the graph to answer the questions).

a. C

b. D

c. None of these answers

d. E

e. A

f. B

Question 3: Check all that apply.

Consider the graph G (V,E) where V is the set of vertices and E is the set of undirected edges. V = {A, B, C, D, E} and E = {(D,C), (E,C), (D,B), (A,D)}.

This graph is maybe a tree rooted at vertex C. Check all properties that apply to this graph.(It would help to draw the graph to answer the questions).

a. binary tree

b. undirected

c. connected

d. acyclic

e. None of these answers

Question 4: Check all that apply.

Consider the graph G (V,E) where V is the set of vertices and E is the set of undirected edges. V = {A, B, C, D, E} and E = {(D,C), (E,C), (D,B), (A,D)}.

If this graph is a tree and rooted at vertex D, then these nodes are leaves. (It would help to draw the graph to answer the questions).

a. None of these answers

b. D

c. B

d. A

e. C

f. E

Question 5: Numerical Answer.

Consider the graph G (V,E) where V is the set of vertices and E is the set of undirected edges. V = {A, B, C, D, E, F, G} and E = {(D,C), (E,A), (D,B), (E,B), (G,D), (E,F)}.

If this graph is a tree and rooted at vertex F, then this tree has a height equal to __________ . (It would help to draw the graph to answer the questions).