5 Let G = (V, E) be a digraph in which every vertex is a source, or a sink, or both a sink and a source. (a) Prove that G has neither self-loops nor anti-parallel edges. (b) Let Gu = (V, Eu) be the undirected graph obtained by erasing the direction on the edges of G. Prove that G" has chromatic number 1 or 2.

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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5
Let G (V, E) be a digraph in which every vertex is a source, or a sink, or both a
sink and a source.
(a)
Prove that G has neither self-loops nor anti-parallel edges.
(b)
Let Gu
=
(V, Eu) be the undirected graph obtained by erasing the direction on
the edges of G. Prove that G" has chromatic number 1 or 2.
You are not required to draw anything in your proofs.
Transcribed Image Text:5 Let G (V, E) be a digraph in which every vertex is a source, or a sink, or both a sink and a source. (a) Prove that G has neither self-loops nor anti-parallel edges. (b) Let Gu = (V, Eu) be the undirected graph obtained by erasing the direction on the edges of G. Prove that G" has chromatic number 1 or 2. You are not required to draw anything in your proofs.
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