Prove the following and make a sketch. a) Prove that every Eulerian graph of odd order has three vertices of the same degree. b) If every vertex in a graph G is even, no edge in that graph is a bridge.

Prove the following and make a sketch. a) Prove that every Eulerian graph of odd order has three vertices of the same degree. b) If every vertex in a graph G is even, no edge in that graph is a bridge.

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

Prove the following and make a sketch.
a) Prove that every Eulerian graph of odd order has three vertices of the same
degree.
b) If every vertex in a graph G is even, no edge in that graph is a bridge.

Please make a sketch.Thank you

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