In an undirected graph, the degree d(u) of a vertex u is the number of neighbors u has, or equivalently, the number of edges incident upon it. in a directed graph, we distinguish between the indegree din(u), which is the number of edges into u, and the outdegree dout(u), the number of edges leaving u.

(a) show that in an undirected graph, σuₑvd(u) = 2| e |.
(b) use part (a) to show that in an undirected graph, there must be an even number of vertices whose degree is odd.
(c) does a similar statement hold for the number of vertices with odd indegree in a directed graph?

Why the bear has a slunky tail determine the meaning of the word slunk in the story

You have a linux system that has a 1000gb hard disk drive, which has a 90gb partition containing an ext4 filesystem mounted to the / directory and a 4gb swap partition. currently, this linux system is only used by a few users for storing small files; however, the department manager wants to upgrade this system and use it to run a database application that will be used by 100 users. the database application and the associated data will take up over 200gb of hard disk space. in addition, these 100 users will store their personal files on the hard disk of the system. each user must have a maximum of 5gb of storage space. the department manager has made it very clear that this system must not exhibit any downtime as a result of hard disk errors. how much hard disk space will you require, and what partitions would you need to ensure that the system will perform as needed? where would these partitions be mounted? what quotas would you implement? what commands would you need to run and what entries to /etc/fstab would you need to create? justify your answers.

Which of these is a benefit of using objects in a powerpoint presentation? a. collaborators can create the external files while you create and edit the slide show. b. you can easily change the theme and design of the presentation. c. you can have older data in the source file while having up-to-date data in the presentation. d. collaborators can easily share the presentation.