 # Math Anonymous

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Handout 21 COMP 163: Discrete Structures, Spring 2018 Nathan Lopez Loyola University, Computer Science Department Problem Set #7 Issued April 9, 2017 Due at 2:00pm on April 20, 2017 1. Consider the following graph with V = {A, B, C, D, E, F } and E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. A F 2 1 3 4 B 5 6 D 8 9 7 C (a) (b) (c) (d) (1 (1 (1 (1 point) point) point) point) E 10 11 Find all pairs of parallel edges. Find all loops. Find all isolated vertices. What vertices are incident on edge 4? 2. (a) (4 points) Draw the complete bipartite graph K2,5 . (b) (3 points) How many edges are in K2,5 ? (c) (5 points) For arbitrary integers m, n 1, how many edges are in the complete bipartite graph Km,n ? 3. Consider the following graph G: T U Y W V Z X 1 (a) (7 points) Find the degree of each vertex in G. (b) (5 points) Does G has an Euler cycle? Why or why not? 4. Consider the following graph: A B C (a) (5 points) Find the adjacency matrix M . (b) (3 points) Calculate M 3 (you do not have to show your work for this, you may use a calculator or other program to compute this matrix multiplication). (c) (3 points) Use M 3 to find the number of paths of length 3 from A to B. 5. Consider the following tree with root a: a c b e d f (a) (3 points) Find the level of each node. (b) (3 points) Find the height of the tree. 2 6. (5 points) Use any algorithm to find a spanning tree of the following graph. Designate the root of your spanning tree. You do not have to show your work. T U Y W V Z X Total: 50 points 3 ...
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KatherineMoran
School: Cornell University  Attached.

Question 2.

Question 4.

(a) Adjacency matrix M of graph G
A

B

C

0 1
1 0
1 0

1
0
0

0 1
1 0
1 0

1
0
0

0 1
1 0
1 0

1
0
0

0 1
1 0
1 0

1
0
0

2 0
0 1
0 1

0
1
1

0 1
1 0
1 0

1
0
0

0 2
2 0
2 0

2
0
0

(b) Calculate M3 =

=

The final...

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