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Math / Discrete Mathematics 1 / Chapter 15 / Problem 2

Discrete Mathematics | 1st Edition | ISBN: 9781577667308 | Authors: Gary Chartrand, Ping Zhang

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There are eight students in a graduate computer science class. Each student has a web

Chapter 15, Problem 2

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QUESTION:

There are eight students in a graduate computer science class. Each student has a web page and each web page has a link to exactly two web pages of other students in the class. Show that for each student s, there exists a student s such that (1) there is no link from the web page of s to the web page of s and (2) for each student s for whom there is a link from the web page of s to the web page of s, there is no link from the web page of s to the web page of s.

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QUESTION:

There are eight students in a graduate computer science class. Each student has a web page and each web page has a link to exactly two web pages of other students in the class. Show that for each student s, there exists a student s such that (1) there is no link from the web page of s to the web page of s and (2) for each student s for whom there is a link from the web page of s to the web page of s, there is no link from the web page of s to the web page of s.

ANSWER:

Problem 2

There are eight students in a graduate computer science class. Each student has a web page and each web page has a link to exactly two web pages of other students in the class. Show that for each student s, there exists a student s such that (1) there is no link from the web page of s to the web page of s and (2) for each student s for whom there is a link from the web page of s to the web page of s, there is no link from the web page of s to the web page of s.

Step by Step Solution

Step 1 of 3

According to the data given, there are 8 students and each student has a web page.

And further each web page has a link to exactly two web pages of another student’s web page.

Let them be numbered from 1 to 8.

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