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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 57E

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part 1 2 e graph theory

s. Show that AUB‡V(G)
Exercice 3.
Consider a connected graph G and let e = uv € E(G) such that G' = G-e is disconnected.
Let G₁ and G₂ be two induced subgraphs of G such that V(G₁) = {x € G: G' contains an ru-path}
and V(G₂) = {x € G: G' contains an ru-path}.
(1) Show that G₁ and G₂ are both connected.
(2) Show that V(G) = V(G₁) UV(G₂).
(3) Deduce that G' contains only two connected components.

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