Intro to Tree Graphs | Trees in Graph Theory, Equivalent Definitions

[@WrathofMath]

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! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Graph Theory course: kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH Graph Theory exercises: kzbin.info/aero/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L

[@vyomsethia5986]

4 years later, still the best explanation on KZbin

[@WrathofMath]

Damn I’m old

[@white-cz4uw]

It's weird that you don't have a lot of views. I'm studying graph theory, and your explanations are the best that I found.

[@WrathofMath]

Thanks so much! KZbin has a lot of math lessons, so it takes most of my videos a good chunk of time to pick up momentum. I'm so glad you've found the lessons helpful, and if you know anyone who would benefit from them you can help them pick up that growth by sharing them around! Let me know if you ever have any questions!

[@jirrs]

I finally understand the different between tree and forest. Thank you for the video.

[@k_nito7954]

7:08 cracked me up haha. Great video by the way, I've been binging all your graph theory videos for my midsem tomorrow

[@arrigune]

Man, you're the best online free teacher I've had.

[@suyashsharnagat2912]

Keep continue making such helpful videos sir Ya it's being a patience for you but Definitely people will come here too... Don't stop uploading.. Loved the channel From india 😁

[@WrathofMath]

Thank you for watching and for your kind words! :) I will not stop creating math lessons until I drop dead, you have my word!

[@hargunsinghkhera1952]

@@WrathofMath Really Awesome videos even I am also watching from India 😁

[@user-jc5vo9sz3l]

​@@WrathofMath me toooooo

[@Sirjio]

Great explanation! Your clarity on the concept of trees in graph theory and the equivalent definitions makes it much easier to grasp. Looking forward to more lessons. Keep up the excellent work!

[@Spacexioms]

it would be awesome to combine all your graph theory lectures in one video along with time stamps!

[@springvibes5344]

I love the way you explaining Graph Theory ^^. This is the definition of Passion. Thank you.

[@WrathofMath]

Thank you so much!

[@HighlandCatz]

this is the go-to channel for discrete math

[@Intrepidsivi]

Thank you so much for explaining tree in most simple form.

[@junior632]

just the best content about graphs on youtube

[@salatenn]

Best teacher I ever seen! . Sir your explanation is very easy to understand. Thank you sir ❤️

[@WrathofMath]

Thank you so much! I am glad it helped, and let me know if you ever have any questions!

[@salatenn]

@@WrathofMath no question till now from your graph theory playlist sir, if I have I will let u know. ❤️❤️❤️

[@_justsam3605]

i love you , you will be the reason i pass this course

[@Sirjio]

00:00 Definition: A tree in graph theory is a connected graph with no cycles. 02:42 Equivalent Definition: A tree is a connected graph where the size is one less than the order. 04:42 Forest Concept: A forest is a graph whose components are all trees; adding an edge to disconnect the graph still makes it a forest. 05:39 Equivalent Definition: In a tree, every two vertices are connected by exactly one unique path. 07:26 Leaf in a Tree: A leaf is a vertex with degree 1 in a tree; leaves are vertices with only one incident edge. 08:52 Proving Concepts: To prove a path graph is a forest, show it's connected and has no cycles; paths with end vertices can't be part of a cycle. 09:29 Challenge: Prove the equivalence between the definition of a tree and the condition that every pair of vertices is connected by exactly one unique path.

[@beepbeep767]

its such a pleasure listening to you :)

[@mathematicalsciences3855]

I am not seen teacher like you in youtube..

[@xxxxxxv6766]

your lessons have been the most helpful to me thank you for your work

[@WrathofMath]

So glad they have helped, thanks for watching and let me know if you ever have any questions!

[@EraadAhmed]

thank you for making these videos, helpful for my discrete structures course

[@WrathofMath]

You're very welcome!

[@samyakmishra7107]

Maan u deserve a lot more views and likes for this good content👌👌👌🔥🔥

[@WrathofMath]

Thank you, Samyak! I've got more on the way! The next video will be a documentary, I hope you'll tune in!

[@abdullahhassan479]

Thank you very much, loved you explanation 🙏🙏

[@codemathlab]

Thank you so much for these videos.

[@yashanmaduwantha4945]

Very Good Explanation

[@WrathofMath]

Thank you!

[@saeid4349]

Your demonstration of tree is much more looking like the one in the movie of "House of dead" :-)

[@gnisitricks]

Good video! :) Greetings from Germany!

[@WrathofMath]

Thanks for watching and I am glad it was clear!

[@pwintphyu4775]

Could u please answer me ? Is a path tree?

[@Djougoune-Beriasso]

How can I explain the theory of a binary search tree?

[@hinatachan_1198]

helpful videos sir thank you !!

[@WrathofMath]

You're very welcome! Thanks for watching and I am glad you're finding them helpful!

[@dariyanagashi8958]

Thank you for this video lesson!

[@omatron22]

whats the song in the outro called? I cant find it in vallows discography.

[@WrathofMath]

Good question! It is "Backdrops". You can find an early version of the song in his Castasides collection on Bandcamp. The version in this video is from his album "Of a Flower Past its Prime", which is no longer available anywhere. I'm not even sure I still have it anywhere unfortunately.

[@TheAkhilamascreen]

You are a lifesaver !

[@WrathofMath]

Glad to help! Thanks for watching!

[@TheBrainixAcademy]

Plzz upload videos on level function of a rooted tree.

[@sabeehaalkhafighy538]

Hi thank you free much do have any videos about domination and about changing and unchanging domination please I want you to answer quickly

[@WrathofMath]

Glad to help! I don't have any videos about domination. I plan to make some, but I haven't read about changing and unchanging domination I don't think, I'd have to look into it.

[@TravLong]

whats the name of the outro song

[@WrathofMath]

I think that was Pins and Pine Needles from Vallow's (now Crayon Angel's) album "Of a Flower Past its Prime". The album was originally released under the "No But Yeah" moniker I think, and is no longer available anywhere I am sad to say. Here is his bandcamp if you wanna hear his other stuff: crayonangel.bandcamp.com/music Check out "remains" from Estrella.

[@mohammednurhussen1746]

Well explained!

[@WrathofMath]

Thank you, Mohammed!

[@samsunnahar9175]

THANKS A LOT SIR!!

[@WrathofMath]

Glad to help, thanks for watching!

[@solawo]

Love u❤, so cool

[@harshanagovindu87]

Thank You 😁😀👍

[@WrathofMath]

No problem 👍

[@melbens3]

Thank you

[@LunaSmith-i4u]

thank you, so very much!

[@WrathofMath]

Glad it helped!

[@ahmetkarakartal9563]

thank you soooooooooo much

[@debbieryan8433]

Helpful! Helpful! Helpful!

[@WrathofMath]

Glad to hear it, thanks for watching!

[@Kaviyugamithran]

Also say about tree decompositions in graph theory.......

[@kartikeyvishnoi2978]

Is a tree directed or undirected? I'm confused my professor said it's directed.

[@WrathofMath]

Thanks for watching and that's a fine question! I don't think I mentioned the possibility of directed trees in this video, but you could consider directed trees if you wanted to. You can take a tree and assign a direction to each of its edges, this would be an "orientation" of the tree graph, but I have never heard of trees being defined as directed graphs in general, I don't know of any universal definition used for "directed tree graph". The problem with "directed tree graph" is that it might refer to an orientation of a normal tree graph (as I described above, this is just assigning one direction to each edge of a tree), or it could refer to a directed graph with no directed cycles. Suppose we go with the second definition. Then consider the directed graph with vertices a, b, and c, and directed edges (a, b), (b, c), and (a, c). This is a directed graph with no directed cycles. However, if we were to remove direction from the edges and consider the underlying undirected graph, that is the cycle graph on 3 vertices. This isn't necessarily a problem, but it certainly is strange! Point is - tree graphs are undirected. If your professor is saying a tree is a type of directed graph then 1) you're in a weird graph theory course haha and 2) make sure you understand precisely the definition he is using, because it's not the conventional usage of the term. Hope that helps!

[@charlesamofordjuoh9940]

How do you find the center of the tree

[@WrathofMath]

Thanks for watching, Charles, and good question! I don't know a lot about centers of trees but I try to answer your question in this new video: kzbin.info/www/bejne/ooGXnId5eadobqc around the 40:38 mark

[@PunmasterSTP]

0:50 trunk

[@shahdmohammed9514]

You're perfect

[@WrathofMath]

Thank you, I try my best! 😊

[@yangxia6011]

If you're into film study, you'll love those jump cuts. lol

[@pwintphyu4775]

Hello sir . Could u answer me pls? Is a path tree?

[@WrathofMath]

Thanks for watching and for the question! Ask yourself this: is a path graph connected? Does a path graph contain cycles? If it is connected and does not contain cycles then it is a tree, so what do you think?

[@AbdulAziz-yr6jf]

Why graph is more useful than tree? Plz explain argently, thank you

[@NamutebiEdith-j4z]

Another videos continueing from there where this one has just stopped

[@chrisrainville6324]

Tony stark would be proud!

[@Delzaleon]

u look so much like my teacher

[@WrathofMath]

Thanks for watching! And that's funny, is your teacher good?