Proof: Graph is a Tree iff Unique Paths for Each Vertex Pair

Proof: Graph is a Tree iff Unique Paths for Each Vertex Pair | Graph Theory, Tree Graphs

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Wrath of Math

Күн бұрын

Пікірлер: 21

@PunmasterSTP 8 ай бұрын

Unique paths for each vertex pair? More like "Awesome information that we really like to hear!" 👍

@martin_skachkov6016 3 жыл бұрын

I can't say how much i appreciate your videos! They really help me since I am not that good at discrete math. THANK YOU!

@WrathofMath 3 жыл бұрын

Thanks so much, Martin! I'm glad they've been so helpful, and hope they will continue to be. Please let me know if you ever have any questions!

@tdrawdy2 3 жыл бұрын

I'm doing complex analysis right now as well, so I would love to see videos on that subject.

@WrathofMath 3 жыл бұрын

Thanks for watching and I'd love to make complex analysis videos! I definitely will sometime, but it will probably be a while, there is much I need to finish first!

@spartanind 4 жыл бұрын

Nice explanation. I've an exam on algebra two days later. No doubt now persists in mind. God bless you! One request is that I am an undergraduate student of mathematics and I wanna learn concepts deeper as well as exercise more n more, too. Can you please suggest me some books of college level for pure mathematics?

@davidshi451 3 жыл бұрын

Great video! Although I prefer algebra, I think tree graphs might be my favorite part of graph theory, the proofs are always so charming!

@WrathofMath 3 жыл бұрын

Thanks, David! I have similar feelings. I love the plain rigor of algebra, with all of its symbols and operations. In graph theory I think it can sometimes be a bit hard to understand exactly when a proof is complete, especially for beginners, since so much of our thought is devoted to visual interpretation of objects that are literally just sets. Tree graphs though, are easy to draw, and operate under a pretty strict set of rules. They have lots of cool properties, and are definitely a highlight of graph theory for me as well! Another cool result concerning tree graphs is how every connected graph has a spanning tree. It's obviously true when you think about it, but just another way tree graphs show their importance! Proof of that if you're interested (warning it is a spooky video): kzbin.info/www/bejne/Y3TEkKiGlNyFppY

@davidshi451 3 жыл бұрын

@@WrathofMath Thank you, I'll check it out! And yeah, I think algebra has been easier for me because it "compresses" better. As in, there are a few core ideas that you study deeply, and they're tightly connected. Whereas graph theory feels more...scattered. Ironically, the visual nature of graphs sometimes feels like more of an obstacle than an advantage!

@paradigmnnf 2 жыл бұрын

Algebra has a very limited capability to capture the world of combinatorics. Graph theory can capture almost everything under the sky! Another "view": a-picture-is worth-a thousand-words also applies to graph theory vs. algebra.

@annakbanana861 Жыл бұрын

is this the same proof where if T is a tree, we prove that for any two distinct vertices v and w of T, there is exactly one path from v to w in T?

@jaehongcho5782 4 жыл бұрын

Just want to clarify the definition of distinct path. Say , are paths in a tree, should I consider these two the same or this would be a counter example for a statement, if a graph is a tree then there is exactly one path between every pair of vertex?

@WrathofMath 4 жыл бұрын

Thanks for watching, Jaehong, and good question! When I use the term "path" I am referring to what is sometimes called a simple path, this is a walk (a sequence of adjacent vertices) that repeats no vertices. So the second example you give is not a path by this definition, thus the theorem holds. Does that help?

@jaehongcho5782 4 жыл бұрын

@@WrathofMath It is clear! Thank you so much for the quick response and the awesome videos!

@sayanmitra9934 4 жыл бұрын

hey! wrath of math.. can you make some videos on determination of roots of a quadratic equation from its graph (different cases and different scenarios)