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

If this graph is a tree and rooted at vertex B, then the tree rooted at Vertex B has these properties. (It would help to draw the graph to answer the questions).

a. complete

b. acyclic

c. connected

d. None of these answers

e. binary tree

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

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

a. connected

b. acyclic

c. binary tree

e. None of these answers

f. undirected

Question 3:

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 E, then this tree has a height equal to __________. (It would help to draw the graph to answer the questions).

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 = {(A,D), (D,C), (E,B)}.

If this graph includes cycles, check all vertices belonging to a cycle. (It would help to draw the graph to answer the questions).

a. D

b. A

c. E

d. B

e. C

f. None of these answers