Must show all work to get 5 stars 1. In a company, emails sent from one employee

Question

Must show all work to get 5 stars

1. In a company, emails sent from one employee to another are tracked as follows:style='font-family: "times new roman","serif"; font-size: 14pt;'>

Mr. Cooper sends 3 emails to Mrs. Sanders. Mrs. Sanders sends 4 emails to Ms. Bighton,>

Ms. Bighton send 1 email to Mr. Ortega and Mr. Ortega does not send anyone any emails.>

Furthermore, Mrs. Sanders sends Mr.Cooper 3 emails, Mrs. Bighton sends Mr. Cooper 2 emails.

(a) Draw a graph to represent connections within this company,>

based on email data, where each vertex represents a person and an edge joining two verticesstyle='font-family: "times new roman","serif"; font-size: 14pt;'>

represents the presence or absence of email communication between them (in either direction).

style="font-size: 12px;">

(b) Find the beta index of the graph you found in part (a).style="font-size: 12px;">

style="font-size: 12px;">

2. You and a friend meet three other couples at a party and several handshakes take place.style="font-size: 12px;">

Nobody shakes hands with himself or herself, there are not handshakes within couples,>

and no one shakes hands with the same person more than once. The numbers of hands

shaken by the other seven people (excluding you) are all different.

How many hands did you shake? How many hands did your partner shake?

Use a graph to aid your solution

Section 9.2:style="font-size: 12px;">

1. Draw a pseudograph to represent the email communication graph described in exercise 1 (Section 9.1) abovestyle="font-size: 12px;">

. In your pseudograph, each vertex represents a person and an directed edge joining two vertices representsstyle="font-size: 12px;">

an email sent.
style="font-size: 12px;">

2. Consider the graph you drew for exercise 1, section 9.1 above (emails). Is this a complete graph? Why

or why not? If not, explain how you could "complete the graph" by adding an edge or edges. Is this

a bipartite graph? Why or why not? If not, explain how you could "make the graph bipartite" by

removing an edge or edges (find a bipartite subgraph).

3. Use the Handshake Theorem (Proposition 9.2.5) to solve the following problem.

Suppose that you arrive at a gathering of 8 people. Suppose that upon your arrival,

you learn two facts: that 12 handshakes have already taken place and that

every person participated in the same number of handshakes, h.

How many hands did each of the 8 people shake? (Find h).

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Explanation / Answer

2) both have 6*4 = 24 handshake

multiplie by 4 because two person handshake 4 ways

1

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