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d. Add up all the indegrees, and add up all the outdegrees. What do you notice? Can you explain why every directed graph must have this property?

d. Add up all the indegrees, and add up all the outdegrees. What do you notice? Can you explain why every directed graph must have this property?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Discrete math. Please answer part d of this problem and please do not reject. 

d. Add up all the indegrees, and add up all the outdegrees. What do you notice? Can you explain why every directed graph must have this property?
Transcribed Image Text:d. Add up all the indegrees, and add up all the outdegrees. What do you notice? Can you explain why every directed graph must have this property?
In the diagram, each vertex represents a web page focused on twelve-tone music. The arrows illustrate links between these web pages. An arrow from vertex \( x \) to vertex \( y \) signifies a hyperlink from web page \( x \) to web page \( y \). ### Diagram Details: - **Vertices**: The diagram includes the vertices labeled as A, B, C, D, E, F, G, H, and I. - **Arrows (Directed Edges)**: - A links to B, C, H, and G. - B links to C and I. - C links to D and F. - D links to C, G, and E. - E links to F. - F links to I. - G links to H and E. - H links to A. - I links to G. This directed graph allows the visualization of how each page is connected, providing an overview of the network of web pages related to the topic.
Transcribed Image Text:In the diagram, each vertex represents a web page focused on twelve-tone music. The arrows illustrate links between these web pages. An arrow from vertex \( x \) to vertex \( y \) signifies a hyperlink from web page \( x \) to web page \( y \). ### Diagram Details: - **Vertices**: The diagram includes the vertices labeled as A, B, C, D, E, F, G, H, and I. - **Arrows (Directed Edges)**: - A links to B, C, H, and G. - B links to C and I. - C links to D and F. - D links to C, G, and E. - E links to F. - F links to I. - G links to H and E. - H links to A. - I links to G. This directed graph allows the visualization of how each page is connected, providing an overview of the network of web pages related to the topic.
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