6. Prove that the number of vertices in an undirected graph with odd degree must beeven. Hint. Prove by induction on the number of edges.7. Suppose you had to color the edges of an undirected graph so that for each vertex, theedges that it is connected to have different colors. How can this problem betransformed into a vertex coloring problem?

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6. Prove that the number of vertices in an undirected graph with odd degree must be even. Hint. Prove by induction on the number of edges.

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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Question

6. Prove that the number of vertices in an undirected graph with odd degree must be
even. Hint. Prove by induction on the number of edges.
7. Suppose you had to color the edges of an undirected graph so that for each vertex, the
edges that it is connected to have different colors. How can this problem be
transformed into a vertex coloring problem?

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