Hon Discrete CHAPTER 7 Practice Multiple Choice

Hon Discrete CHAPTER 7 Practice Multiple Choice: 1) Which of the four graphs pictured below are trees?

Graph #1 Graph #2 Graph #3 Graph #4 A) Graph 2 B) Graph 2 and 4 C) Graph 2 and 3 D) Graph 2, 3, and 4 E) None of the Above

2) Which of the four graphs pictured below are not trees?

Graph #1 Graph #2 Graph #3 Graph #4 A) Graph 3 B) Graph 2 and 4 C) Graph 2 and 3 D) Graph 1 and 3 E) None of the Above

3) The number of vertices in a tree with 12 edges is A) 10 B) 11 C) 12 D) 13 E) None of the above

4) Assume graph G has no loops or multiple edges. Which of the following graphs are definitely trees? A) G has 9 vertices and 8 bridges. B) G has 11 vertices and 9 edges C) G has 7 vertices and no circuits. D) All of the above graphs are trees. E) None of the above graphs are trees.

5) The number of edges in a tree with 32 vertices is A) 30 B) 31 C) 32 D) 33 E) None of the above

6) Suppose a graph has 15 vertices and 14 edges. Then A) Graph must be a tree. B) Graph is either a tree or it is not connected. C) G cannot have any circuits. D) G cannot have more than one path joining any two vertices. E) None of the above. 7) How many spanning trees does the graph in Figure #1 have? A) 3 B) 4 C) 5 D) 8 FIGURE #1 E) None

8) How many spanning trees does the graph in Figure #2 have? A) 10 B) 15 C) 23 FIGURE #2 D) 24 E) None

9) How many spanning trees does the graph in Figure #3 have? A) 11 B) 55 C) 59 FIGURE #3 D) 60 E) None

10) How many spanning trees does the graph in Figure #4 have? A) 19 B) 20 C) 392 FIGURE #4 D) 419 E) 420

D For # 11 and 12, use Figure #5. 171 81 11) Using Kruskal’s algorithm, which edge should you choose second? 92 140 A) AE B) AB C E C) BD D) DE 250 E) None of the above 163 142 ______12) Using Kruskal’s algorithm, 63 which edge should you choose fourth? 261 A) AB B) BC C) BD D) DE B 134 A E) None of the above FIGURE #5 HONORS DISCRETE CHAPTER 7 REVIEW 1) Identify if each graph is a tree or is not a tree.  If possible, find a spanning tree in the network.  Calculate the redundancy of each graph

GRAPH #1 GRAPH #2

GRAPH #3 GRAPH #4

2) How many possible spanning trees exist in the network?

Network #1 Network #2 Network #3

Network #4 Network #6 Network #5 4) Determine if the follow descriptions of a graph are (1) ALWAYS A TREE, (2) NEVER A TREE, or (3) SOMETIMES A TREE. #1: 9 vertices and 8 edges. #5: 14 vertices and 12 bridges.

#2: 5 bridges and 6 vertices. #6: Only one path exists between any two vertices in the graph.

#3: 18 edges and 17 vertices. #7: Connected graph with Redundancy = 0

#4: 7 vertices and no circuits #8: 5 edges and 5 vertices.

5) Find the minimum spanning tree using Kruskal’s algorithm and provide the overall weight of the MST.

D 50 E A 1.3 B 3.8 C 90 100 90 60 1.4 1.7 1.5 2.2 3.0 H 2.4 D 120 80 80 2.3 50 50 2.3 1.6 I C D FE 2.1 90 100 1.2 140 110 40 G 90 60 2.6 3.6 3.1 2.8 60 120 8090 80 2.9 J 1.6 50 C F 140 110 40 F 4.1 E B 60100 A 90

B 100 A