Proof: Graph with all Even Degree Vertices has no Bridges | Graph Theory

A connected graph whose vertices all have even degree has no bridges! We will prove this result in today's graph theory lesson!
The proof follows pretty easily using contradiction, the definition of bridge, and some simple graph theory results we have previously proven. We'll use an argument about the parity (even or odd) of the sum of the degrees of the vertices in a subgraph of our graph.
Lesson on First Theorem of Graph Theory: • The First Theorem of G...
Proof every graph has an even number of odd degree vertices: • Proof: Every Graph has...
Lesson on bridges: • What are Bridges of Gr...
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a friend of mine named Molly Ponkevitch, who, upon my request, kindly gave me permission to use her music in my outros. I usually put my own music in the outros, but I love Molly's music, and wanted to share it with those of you watching. Please check out her wonderful music and other work, as she also does poetry and more.
Molly's TH-cam: / @mollyponkevitch1512
Molly's Instagram: dyx_soma?h...
Molly's Website: www.mollyponkevitch.com/
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[@szpaswogel8425]

It's a pure pleasure to follow such clear proof. Good job!

[@WrathofMath]

Thank you for watching and for your kind words :) I'm glad you found it clear!

[@PunmasterSTP]

No bridges? More like "No bs!", 'cause these videos are awesome! 👍

[@zehrademirhan600]

Thanks for the proof:) But it was better and more fun to watch when you used the whiteboard . Hopefully more videos will be like that :).

[@user-xn9qt2xq4f]

Nice and clear

[@treadingvid4051]

how do you find the size of the automorphisms?

[@WrathofMath]

Thanks for watching and did this lesson say anything about automorphisms? I don't think it did, so I am just curious what context you're asking this question it. By size of automorphisms I am not sure what you mean. An automorphism is a function from the vertex set back to itself, so the domain's "size" or cardinality is the cardinality of the vertex set which is the order of the graph. Are you asking about the number of automorphisms? That would depend on the graph.

[@treadingvid4051]

@@WrathofMath Yes I'm talking about the number of automorphisms in any graph. Like how do you get them when you're given a graph?