T2.4: Let d₁

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 18E
icon
Related questions
Question
T2.4: Let d₁ <d₂ <d be the vertex degrees of a graph G. Prove that G is connected if
d; ≥ j when j≤n-1-d. That is, every graph having degree sequences with these conditions
will be connected.
Hint - Consider a a component that omits some vertex of maximum degree. Observe also that d₁
is smallest and dr largest degree, reversing our normal notations, as this notation makes the proof
easier.
Transcribed Image Text:T2.4: Let d₁ <d₂ <d be the vertex degrees of a graph G. Prove that G is connected if d; ≥ j when j≤n-1-d. That is, every graph having degree sequences with these conditions will be connected. Hint - Consider a a component that omits some vertex of maximum degree. Observe also that d₁ is smallest and dr largest degree, reversing our normal notations, as this notation makes the proof easier.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage