1: Prove the directed version of Veblen's Theorem : A directed graph admits a decomposition into directed cycles if and only if its even. 2: Show that a graph G is connected if and only if there is an (X,Y) - path in G for any two nonempty subsets X and Y of V.

1: Prove the directed version of Veblen's Theorem : A directed graph admits a decomposition into directed cycles if and only if its even. 2: Show that a graph G is connected if and only if there is an (X,Y) - path in G for any two nonempty subsets X and Y of V.

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

1: Prove the directed version of Veblen's Theorem : A directed graph admits a decomposition into directed cycles if and only if its even.

2: Show that a graph G is connected if and only if there is an (X,Y) - path in G for any two nonempty subsets X and Y of V.

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