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! ua-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin Graph Theory course: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html Graph Theory exercises: ua-cam.com/play/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L.html
Thanks so much! UA-cam 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!
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 😁
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!
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.
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.
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.
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.
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!
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: ua-cam.com/video/lP4kTCDB58E/v-deo.html around the 40:38 mark
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?
![Lp. Сердце Вселенной #1 НАЧАЛО ПУТЕШЕСТВИЯ [Новый сезон] • Майнкрафт](http://i.ytimg.com/vi/380Q7gLWGvk/mqdefault.jpg)
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!
ua-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
Graph Theory course: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Graph Theory exercises: ua-cam.com/play/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L.html
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.
Thanks so much! UA-cam 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!
I finally understand the different between tree and forest. Thank you for the video.
4 years later, still the best explanation on UA-cam
Damn I’m old
Man, you're the best online free teacher I've had.
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 😁
Thank you for watching and for your kind words! :) I will not stop creating math lessons until I drop dead, you have my word!
@@WrathofMath Really Awesome videos even I am also watching from India 😁
@@WrathofMath me toooooo
it would be awesome to combine all your graph theory lectures in one video along with time stamps!
Thank you so much for explaining tree in most simple form.
i love you , you will be the reason i pass this course
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!
this is the go-to channel for discrete math
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.
just the best content about graphs on youtube
your lessons have been the most helpful to me thank you for your work
So glad they have helped, thanks for watching and let me know if you ever have any questions!
Best teacher I ever seen! . Sir your explanation is very easy to understand. Thank you sir ❤️
Thank you so much! I am glad it helped, and let me know if you ever have any questions!
@@WrathofMath no question till now from your graph theory playlist sir, if I have I will let u know. ❤️❤️❤️
I am not seen teacher like you in youtube..
Thank you so much for these videos.
thank you for making these videos, helpful for my discrete structures course
You're very welcome!
helpful videos sir thank you !!
You're very welcome! Thanks for watching and I am glad you're finding them helpful!
Thank you very much, loved you explanation 🙏🙏
Thank you for this video lesson!
Your demonstration of tree is much more looking like the one in the movie of "House of dead" :-)
Good video! :) Greetings from Germany!
Thanks for watching and I am glad it was clear!
Could u please answer me ? Is a path tree?
thank you, so very much!
Glad it helped!
Maan u deserve a lot more views and likes for this good content👌👌👌🔥🔥
Thank you, Samyak! I've got more on the way! The next video will be a documentary, I hope you'll tune in!
Also say about tree decompositions in graph theory.......
How can I explain the theory of a binary search tree?
Plzz upload videos on level function of a rooted tree.
Well explained!
Thank you, Mohammed!
You are a lifesaver !
Glad to help! Thanks for watching!
Thank You 😁😀👍
No problem 👍
Hi thank you free much
do have any videos about domination and about changing and unchanging domination
please I want you to answer quickly
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.
Helpful! Helpful! Helpful!
Glad to hear it, thanks for watching!
thank you soooooooooo much
whats the song in the outro called? I cant find it in vallows discography.
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.
whats the name of the outro song
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.
You're perfect
Thank you, I try my best! 😊
If you're into film study, you'll love those jump cuts. lol
Is a tree directed or undirected?
I'm confused my professor said it's directed.
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!
0:50 trunk
How do you find the center of the tree
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: ua-cam.com/video/lP4kTCDB58E/v-deo.html around the 40:38 mark
Why graph is more useful than tree? Plz explain argently, thank you
Hello sir . Could u answer me pls? Is a path tree?
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?
u look so much like my teacher
Thanks for watching! And that's funny, is your teacher good?
Tony stark would be proud!