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, 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 B, then the subtree rooted at Vertex E include these vertices. (It would help to draw the graph to answer the questions).

a. G

b. C

c. A

d. None of these answers

e. E

f. D

g. F

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), (D,B), (E,B), (A,D)}.

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

a. None of these answers

b. D

c. A

d. B

e. E

f. C

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), (C,E), (B,D), (E,B)}.

Check all properties that this graph has. (It would help to draw the graph to answer the questions).

a. None of these answers

b. acyclic

c. undirected

d. connected

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, 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 B, then this tree has these properties. (It would help to draw the graph to answer the questions).

a. connected

b. None of these answers

c. binary tree

d. acyclic

e. complete