Access over 20 million homework documents through the notebank

Get on-demand Q&A homework help from verified tutors

Read 1000s of rich book guides covering popular titles

Anonymous

can you please answers questions 2,4,5,6.............................please I want to get full marks

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
...

Purchase answer to see full attachment

Purchase answer to see full attachment

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...

Review

Anonymous

Top quality work from this tutor! I’ll be back!

Anonymous

It’s my second time using SP and the work has been great back to back :) The one and only resource on the Interwebs for the work that needs to be done!

Anonymous

Thanks, good work

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors