Let G be a graph on n vertices (with no loops or multiple edges). Prove that if all vertices in G have different degrees, then n = 1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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Let G be a graph on n vertices (with no loops or multiple edges). Prove that if all vertices
in G have different degrees, then n = 1.
Transcribed Image Text:Let G be a graph on n vertices (with no loops or multiple edges). Prove that if all vertices in G have different degrees, then n = 1.
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