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Let G and H be two graphs such that V(H) ≤ V(G). Show that H is an induced subgraph of G if and only if for all x € V (H), N₁(x) = Ng(x)n V(H).

Let G and H be two graphs such that V(H) ≤ V(G). Show that H is an induced subgraph of G if and only if for all x € V (H), N₁(x) = Ng(x)n V(H).

Advanced Engineering Mathematics
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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Let G and H be two graphs such that V(H) ≤ V(G). Show that H is an induced subgraph of G if and only if for all x € V (H), Nµ(x) = Ng(x) ^ V (H).
Transcribed Image Text:Let G and H be two graphs such that V(H) ≤ V(G). Show that H is an induced subgraph of G if and only if for all x € V (H), Nµ(x) = Ng(x) ^ V (H).
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