Proof: Every Graph has an Even Number of Odd Degree Vertices | Graph Theory

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How do we prove that every graph has an even number of odd degree vertices? It seems like a surprising result, how could it be that every graph has such a neat little property? In this video graph theory lesson, we'll prove that every graph has an even number of odd degree vertices, to understand just why it's true!

If you're taking a course in Graph Theory, or preparing to, you may be interested in the textbook that introduced me to Graph Theory: “A First Course in Graph Theory“ by Gary Chartrand and Ping Zhang. It’s a wonderful text! You can purchase this book through my Amazon affiliate link below! Using the affiliate link costs you nothing extra, and helps me continue to work on Wrath of Math!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+

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Support the production of this course by joining Wrath of Math as a Channel Member for exclusive and early videos, original music, and upcoming lecture notes for the graph theory series! Plus your comments will be highlighted for me so it is more likely I'll answer your questions!

WrathofMath
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its very helpfull for my assigment thank you so much <3

laili
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Such a nice explanation. Discrete mathematics is a tough subject. Respect for anyone in this field.

nishantverma
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Just discovered your channel and I am so thankful. Your explanations are on point and you make it easy to follow you. So a big THANKS for that.
As for me, I really like these graph theory proofs, as there are not too many videos that cover that.. So I personally would appreciate even more videos of proofs.
Much love from norway

sophiabnrm
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A light bulb just went off in my head...This is a great explanation!

anjolaadeyemi
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i want recurrence relation for t(n) = t(n/2) +n and find t(60) where t(1)=1 and thank you

mohamedzayton
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Great explanation of an elegant proof! Just curious, will you be doing more algorithms? They keep popping up in my graph theory classes.

davidshi
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These videos are definitely odd...with how good they are!

PunmasterSTP
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what is even an odd degree? why is that important? I didn't understand past the sum of all degrees = 2e

zaman.tasiin
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I can't even believe that this channel isn't famous! Your explanations are simple, logical, and neat. You really show how math is built up from basic logic all the way up to this masterpiece.
If it weren't for you I wouldn't have loved graph theory. Can't wait to see a playlist about Topology, maybe then it'll finally grow on me ... 😂

propea
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Amazing.... Really satisfied from Bangladesh 🥰🥰🥰🥰

rehnumahtaslimmunmun
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that proof was sweet. didn't even need to stop the video and think about any of its parts. I've always liked solving equations, but never really cared about creating them from a word problem, pure math might be for me

luciano
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Thank you for teachibg graph theory easy for us. Is there a chance that you give some undergrad research topic in graph theory?

salamatarvhy
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I found a solution at age 16 in less than 3-7 seconds that is much more obvious than your given solution. I don't tell people about it much because I like to test new people on it. No one can solve it, yet it is spectacularly simple. Your solution is tedious, to be honest. Unnecessarily so, I may add.

Lovin_It
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Very well explained..Understood it. Hats off 🥺

iqramirza
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I just discovered this channel and I must say, you are my savior ☺💕 thaaanka

missmong
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Thanks sir, really helpful before exam

yaaritubevlogs
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Fantastic thanks for making this series

valoraz
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Hi sir, I just want to ask if this is the same with "For any graph G, the sum of degrees of vertices is even."

marcranielnuneza