Question 1

Consider the network shown below; draw two different spanning trees for the network.

Accepted Answer

Here are two possible choices. There
are many more!

Question 2

A local telecommunications company is planning on placing fiber-optic cables along existing roads to network together several towns in a remote area of upstate Vermont. The table below gives the distance in miles between each of the towns via these roads. If it costs the company $1000 per mile to lay down the cable, then find the cost of the cheapest network connecting all of the towns.

Accepted Answer

$51000

Question 3

How many different spanning trees are found in the network shown below?

Accepted Answer

A)  4 
B)  8 
C)  12 
D)  16 
E)  None of the above. 
A)  4 
B)  8 
C)  12 
D)  16 
E)  None of the above. C

Question 4

Consider the graph shown below; what is the weight of the minimum spanning tree of the graph?

Accepted Answer

A)  61 
B)  68 
C)  72 
D)  76 
E)  None of the above. 
A)  61 
B)  68 
C)  72 
D)  76 
E)  None of the above.

Question 5

Consider the network shown in below; how many edges are bridges?

Accepted Answer

The answer of Consider the network shown in below; how...

Question 6

Consider the Graph K shown below; which of the figures shown below are spanning trees of Graph K?

Accepted Answer

A)  figure 1 
B)  figure 2 
C)  figure 3 
D)  All of the figures. 
E)  None of the above. 
A)  figure 1 
B)  figure 2 
C)  figure 3 
D)  All of the figures. 
E)  None of the above.

Question 7

Which of the graphs shown below are not trees?

Accepted Answer

The answer of Which of the graphs shown below are...

Question 8

Consider the network shown below; draw the minimum spanning tree for this network by applying Kruskal's algorithm.

Accepted Answer

Here is th

Question 9

How many different spanning trees are found in the network shown below?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  None of the above. 
A)  1 
B)  2 
C)  3 
D)  4 
E)  None of the above.

Question 10

In the graph shown below, how many edges are bridges?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  None of the above. 
A)  1 
B)  2 
C)  3 
D)  4 
E)  None of the above.

Question 11

In the graph shown below, how many edges are bridges?

Accepted Answer

A)  3 
B)  4 
C)  5 
D)  6 
E)  None of the above. 
A)  3 
B)  4 
C)  5 
D)  6 
E)  None of the above.

Question 12

Which of the graphs shown below are trees?

Accepted Answer

The answer of Which of the graphs shown below are...

Question 13

Every tree must have at least two vertices of degree one.

Accepted Answer

A)  This statement is always true. 
B)  This statement is always false. 
C)  This statement is only true if there are more than four vertices. 
D)  This statement is only false if there are more than four vertices. 
E)  None of the above. 
A)  This statement is always true. 
B)  This statement is always false. 
C)  This statement is only true if there are more than four vertices. 
D)  This statement is only false if there are more than four vertices. 
E)  None of the above.

Question 14

Which of the graphs below are not trees?

Accepted Answer

A)  Graph I 
B)  Graph 2 
C)  Graph 4 
D)  Both Graph 1 and Graph 4 
E)  None of the above. 
A)  Graph I 
B)  Graph 2 
C)  Graph 4 
D)  Both Graph 1 and Graph 4 
E)  None of the above.

Question 15

A city consists of five boroughs, and each borough has three neighborhoods and each neighborhood consists of ten houses. You have been hired to run a fiber-optic cable, networking all of the houses to each other. No matter the length, it costs $50 to connect any one house to any other house. Based on all of this information, what will it cost to network all of the houses together so that there are no redundancies? Hint: Think of each house as a vertex.
(a) $7450
(b) $7500
(c) $8000
(d) $8500
(e) None of the above.

Accepted Answer

The answer of A city consists of five boroughs, and...

Question 16

What is the redundancy of the complete graph K5 ?

Accepted Answer

The answer of What is the redundancy of the complete...

Question 17

A local telecommunications company is planning on placing fiber-optic cables along existing roads to network together several towns in a remote area of upstate Vermont. The table below gives the distance in kilometers between each of the towns via these roads. If it costs the company $800 per kilometer to lay down the cable, then find the cost of the cheapest network connecting all of the towns.

Accepted Answer

The answer of A local telecommunications company is planning on...

Question 18

What is the redundancy of the graph shown below?

Accepted Answer

A)  6 
B)  7 
C)  8 
D)  9 
E)  None of the above. 
A)  6 
B)  7 
C)  8 
D)  9 
E)  None of the above.

Question 19

How many different spanning trees can be found in the following network?

Accepted Answer

The answer of How many different spanning trees can be...

Question 20

Consider a connected graph with n vertices; if n - 1 of the vertices have degree 1, then the graph is a tree.

Accepted Answer

A)  This statement is always true. 
B)  This statement is always false. 
C)  This statement is always true if and only if one vertex has degree n - 1. 
D)  This statement is only false if and only if one vertex has degree n - 1. 
E)  None of the above. 
A)  This statement is always true. 
B)  This statement is always false. 
C)  This statement is always true if and only if one vertex has degree n - 1. 
D)  This statement is only false if and only if one vertex has degree n - 1. 
E)  None of the above.

Consider the network shown below; draw two different spanning trees for the network.

How many different spanning trees are found in the network shown below?

Consider the graph shown below; what is the weight of the minimum spanning tree of the graph?

Consider the network shown in below; how many edges are bridges?

Consider the Graph K shown below; which of the figures shown below are spanning trees of Graph K?

Which of the graphs shown below are not trees?

Consider the network shown below; draw the minimum spanning tree for this network by applying Kruskal's algorithm.

How many different spanning trees are found in the network shown below?

In the graph shown below, how many edges are bridges?

In the graph shown below, how many edges are bridges?

Which of the graphs shown below are trees?

Every tree must have at least two vertices of degree one.

Which of the graphs below are not trees?

What is the redundancy of the complete graph K5 ?

What is the redundancy of the graph shown below?

How many different spanning trees can be found in the following network?

Consider a connected graph with n vertices; if n - 1 of the vertices have degree 1, then the graph is a tree.

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Exam 7: The Cost of Being Connected

Consider the network shown below; draw two different spanning trees for the network.

How many different spanning trees are found in the network shown below?

Consider the graph shown below; what is the weight of the minimum spanning tree of the graph?

Consider the network shown in below; how many edges are bridges?

Consider the Graph K shown below; which of the figures shown below are spanning trees of Graph K?

Which of the graphs shown below are not trees?

Consider the network shown below; draw the minimum spanning tree for this network by applying Kruskal's algorithm.

How many different spanning trees are found in the network shown below?

In the graph shown below, how many edges are bridges?

In the graph shown below, how many edges are bridges?

Which of the graphs shown below are trees?

Every tree must have at least two vertices of degree one.

Which of the graphs below are not trees?

What is the redundancy of the complete graph K5 ?

What is the redundancy of the graph shown below?

How many different spanning trees can be found in the following network?

Consider a connected graph with n vertices; if n - 1 of the vertices have degree 1, then the graph is a tree.

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The Mathematics of Touring: Traveling Salesman Problems

The Mathematics of Scheduling: Chasing the Critical Path

Population Growth Models: There Is Strength in Numbers

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