Let G be a graph of order n and let k be an integer with 1≤k≤n−1.Prove that if every vertice of G such that deg(v)≥(n+ k − 2)/2, then G is k-connected.

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 of order n and let k be an integer with 1≤k≤n−1.Prove that if every vertice of G such that deg(v)≥(n+ k − 2)/2, then G is k-connected.

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