Graph Theory: 54. Number of Cut-Vertices HD

Notice that the complete graph on n vertices has no cut-vertices, whereas the path on n vertices (where n is at least 3) has n-2 cut-vertices. Can you ever have a connected graph with more than n-2 cut-vertices? The answer is no. We prove that in any non-trivial connected graph there are at least 2 non-cut-vertices. In fact, the proof shows that peripheral vertices of a graph are not cut-vertices. -- Bits of Graph Theory by Dr. Sarada Herke. BIG NEWS - Check out my new course on UDEMY - College Math Essentials: Logarithms https://www.udemy.com/college-math-essentials-logarithms/?couponCode=SaradaYT Related videos: http://youtu.be/BxAgmaLWaq4 - 53 cut-vertices http://youtu.be/YbCn8d4Enos - 51 eccentricity, radius and diameter For quick videos about Math tips and useful facts, check out my other channel "Spoonful of Maths" - http://youtube.com/spoonfulofmaths --- Links --- Website - http://saradaherke.com Facebook - https://www.facebook.com/DrSaradaHerke Twitter - https://twitter.com/SaradaHerke Twitter - https://twitter.com/spoonfulofmaths Google Plus - https://plus.google.com/+SaradaHerke