[Discrete Mathematics] Trees

We look at a subset of graphs called trees.

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[chrissolace]

Thank you for the helpful video!

I had a little trouble at 6:00 but i realized that all you were doing was rearranging (e' = e - 1) and (v' = v - 1) into (e' + 1 = e) and (v' + 1 = v) and then plugged it into the earlier equation (e = v - 1)! It probably took me a bit because I am just a visual learner and I needed to see all the steps. (I'm also typing this out just in case anyone else has the same issue as me later on!)

[badass]

These tutorials have really been very helpful! Thank you sir for explaining the concepts and making them crystal clear! I'm really surprised of the fact that u just have 15k subscribers u seriously deserve to have a lot more.

[tasfiatabassum]

thanks a lot, it really helped me, thank u for giving so much of time in teaching all these topic.

[shoukathali]

I like everything bout this channel except : he doesn't make playlists and I can't find the order to watch the videos.

[hanyi]

if e >= 1 shouldnt there be at least two vertices instead of one?

[anakinkylo.thepomenerianan]

Awesome you can also use Eulers formula to prove a tree has n-1 edges since the region is 1(infinite space) and trees are planar r=e-v+2, r=1 & v=n . However I like the way you proved it makes more senser

[dacianbonta]

@5:16 Whif the vertex has more than one edge coming outta it? well, the graph disconnects, but proving THAT complicates things.
better unleash Euler's Bazooka (v-e+r=2, with r=1). giving the desired answer.
I mean, what's the use of developing Euler's Bazooka (moar like Euler's Panzerfaust, amirite) if you don't use it?

[hinaafzal]

Thnx for uploading all of ur videos are like diamond to me..thnx it helped a lot

[benjaminandersson]

3:01 Do you mean cycle? Or is loop = cycle in your terminology?

[ericgill]

Hey man, what if you delete a vertex with a degree of 2? Doesn't that throw the proof of e=v-1 out of whack? Thanks

[maheshkumargupta]

Show by means of an example that a simple diagraph in which exactly one node has indegree 0 and every other node has indegree 1 is not necessary a directed tree?

[hodgsontetteh]

man i got an A thanks man for yr help

[tryingtolearn]

I am having difficulty with the proof by induction. The basis step talks about |e|=0. and then you show that if the property already holds for some tree, then it'll hold for a **smaller** tree. But this is not the same as the "k+1" step. for this proof to be complete, don't you need to start from the largest possible tree instead of the smallest possible tree?

[maheshkumargupta]

How many different directed trees are there with three nodes ????

[everainbowhue]

all you need is tree(positive space/nursery).

[chetankawarkhe]

which software is this in you video????

[nouwei]

Is it that I am stupid? I can’t understand