1. Prove that in a finite directed graph if every edge has at least one outgoing edge, then the graph contains a cycle. Hint: Consider the longest path in the graph.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 3 Do the following:
1. Prove that in a finite directed graph if every edge has at least one outgoing
edge, then the graph contains a cycle. Hint: Consider the longest path in
the graph.
2. Give an example of a directed graph with infinitely many vertices in which
each verter has at least one outgoing edge, but the graph has no cycles.
Transcribed Image Text:Question 3 Do the following: 1. Prove that in a finite directed graph if every edge has at least one outgoing edge, then the graph contains a cycle. Hint: Consider the longest path in the graph. 2. Give an example of a directed graph with infinitely many vertices in which each verter has at least one outgoing edge, but the graph has no cycles.
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