I am seeing this video after 5 years (2021) . For my semister exams, you explained very clearly . Thank you man
@leechai5679
3 жыл бұрын
same here
@kaustubhupadhyaya6577
3 жыл бұрын
same bro
@Аяулыменжетаева
3 жыл бұрын
Me too
@fortuneprecious2175
3 жыл бұрын
Same here bro😭
@madmaxrex7563
3 жыл бұрын
Same here
@bestyoueverhad.2408
2 жыл бұрын
On my final stretch with discrete maths. Thank you sir. for all you have done, God bles!
@hats5864
5 жыл бұрын
You saved me last year with your tutorials, now it repeats, I was so happy when I saw that you have a course for Graph Theory too. Love you man
@azizchouria4639
3 жыл бұрын
your welcome
@jackmenirons4989
3 жыл бұрын
Case 1: If there is a minimal walk from x to y with no repeated vertices, then it is a path by definition. We are given that w is an element of an x,y walk. Since there are no repeated vertices in this walk, x,y is also an element of the x-y path. Case 2: If there is a walk with repeated vertices, then that walk is not the shortest path (minimal walk) between that x,y pair. We can begin the walk at the repeated vertex to get a shorter walk since that walk will sill include the x,y pair as the start and end points. Then we end up with a walk with no repeated vertices and can apply Case 1.
@Accelerate_CHAOS
2 жыл бұрын
Thanks man
@MMNayem-dq4kd
2 жыл бұрын
Thanks man.
@dreamleaf6784
Жыл бұрын
Thanks man..
@nathanmartinez209
8 ай бұрын
Thanks man...
@Zeliktric
6 ай бұрын
Thanks man....
@tolulopevictor4546
4 жыл бұрын
I'm about to write an online test for a bootcamp, i hope this explains everything i need. But your tutorials so far has been comprehensive especially on Induction
@beccalynn2301
6 жыл бұрын
This video saved my butt. I cannot say enough good things about it. I have been staring at my textbook for 3 hours and I didn’t understand most of it. This video made all the difference in the world.
@vitalispurity9598
5 жыл бұрын
In just few minutes and I understand this better than my maths teacher..thank you
@alizesavim5688
3 жыл бұрын
watching this 6 years later in 2021 and you still saved me with this video. i didnt understand anything when my teacher explained. thank you so much...
@alizesavim5688
2 жыл бұрын
lol i totally forgot that i watched this video and now im retaking this course and watching your video again.
If you have a repeated vertex vi, you may modify the walk by connecting the first edge touching vi with the last one. If this changes the walk then it becomes a shorter walk. If this does not modify the walk, then the first edge is the same as the last one. We can thus make the walk shorter by removing that edge.
@NewtonCazzaro
8 жыл бұрын
Thank you so much! I wish my professor was clear and direct like you are, but unfortunately he stutters and has a thick accent from Russia. I can't understand him and I am taking this class again (with him because he is the only one teaching it in Las Vegas) and I will need you to learn discrete math.....
@Trevtutor
8 жыл бұрын
+Newton Cazzaro (Brazilian Channel) Accents are just one of the many challenges you must overcome to learn math. I wish I were joking :(
@darkdudironaji
5 жыл бұрын
I feel you. I'm actually at UNLV right now struggling with this class. Part of it has to do with the Korean accent of my prof. Hope these videos helped you enough to get you a passing grade, cause I really need it!
@ana-mariagarlau798
3 жыл бұрын
@@darkdudironaji my math prof is native speaker. his issue: he hates his students. he literally sighs once every 2 sentences 🤦♀️, it s so depressing
@haukwantung9832
6 жыл бұрын
This is quoted from my college's lecture notes: " A cycle (or circuit) is a path of nonzero length from v to v with no repeated edges." (It says cycle and circuit share the same meaning if I don't interpret wrongly.) But from your video, this is the definition of circuit ONLY. (For cycle, it should be with no repeated VERTICES). So, can I treat these two terms as the same or not? Thanks! :) By the way, your videos can really help me catch up all the things I can't understand in the lesson. Really great! :)
@giridharkrcomputerscience2848
3 жыл бұрын
I watched these video's after six years . You tought in a very understandable manner thank you so much.
@dc.gamedesigner33
2 жыл бұрын
Im getting ready to start descrete mathematics next tuesday for university and your videos are very helpful.
@aayub
7 жыл бұрын
beautifully explained!
@AbhishekTiwarics
8 жыл бұрын
For the question asked for all walk there exists a path..... for i) point i.e. no repeated vertex then the walk is already a path for ii) when we get a vertex again we delete all vertex from the walk since the vertex was first discovered as from a vertex x->x the x itself is the minimal walk and addition of any edge to traverse same vertex will increase the walk length (contradiction as we are talking about minimal walk) ....thus we get a path for every walk(no vertex repeated) is above explanation correct...?? and your videos are really great...:) thank you
@levyax1964
Жыл бұрын
For reviewing purpose, and got an A in direcrete math. Thank you so much!
@TheOnlyName
Ай бұрын
How am I going to survive this class 😭
@proggenius2024
Жыл бұрын
Thank you man. You are such a brilliant teacher!
@Abohafsah
4 жыл бұрын
Thank you so much trevor, You have just unload a big burden off my shoulder. As i saw the first ten minutes i subscribed it. I will have along way with you from now on... There still one question that really i cant get the idea on how to solve, The questions says: In every directed complete graph, prove that the sums of the squares of the in-degrees (overall vertices) is equal to the sum of the squares of the out-degrees (over all vertices).
@kanchapagimhara3163
4 жыл бұрын
one of the best tutorial I have ever watched on youtube
@sperera5916
8 жыл бұрын
8 isolated vertices disliked this video.
@_kahini
7 жыл бұрын
lol well applied
@cyborg6294
7 жыл бұрын
8 dumbasses disliked this video
@awaisn
6 жыл бұрын
Haha
@suleymanrahimov
6 жыл бұрын
S Perera 😂😂😂
@himal2000
6 жыл бұрын
Make that 30 now m8
@burakaltas668
8 жыл бұрын
Everything is perfectly defined.. Thank you so much! Subscribed :D
@kattarekha3786
3 жыл бұрын
Thank you so much you explained perfectly... I understood it ❤ You helped me a lot
@LilJollyJoker
5 ай бұрын
Amazing!
@mitaanshuagarwal007
8 жыл бұрын
In the example you solved in the end since we have to prove for a simple graph 2e
@FarizDarari
Жыл бұрын
Simply awesome, thanks!
@mengzhuwang7233
3 жыл бұрын
hi for the proof question , if the walk has repeated vertex , it can simply skip the walk around that traingle and get out directly; so clearly there is a shorter walk than the one with repeated vertex. In this case, it contradicts the assumption in saying that w is the shortest walk. Hence, The minimal walk can be path ( no repeated vertex) and thereby , 'there exist x-y path' can be thus proven. Is my thought correct? Thank you!
@xiaoraven2885
5 жыл бұрын
Thanks man , read Lecture notes and bamboozled myself . But this helped
@mndlcoin
11 күн бұрын
I am seeing this video after 9 years (2024). For my mid semister exams. Thank you man
@alperen32
Жыл бұрын
seven years and still saving lives.
@iLeaveYouWithHugs
9 жыл бұрын
Thank you so much for these!
@kosed7041
4 жыл бұрын
In the problem where you have to prove they 2e
@killssingasuka7819
5 жыл бұрын
For all vertices there is an edge. If there was a single vertex there would be no edge and therefore no graph. This continuous way of looking at graphs is more adaptive than viewing them as static things were two vertices are assigned to an edge. Yet two vertices are necessarily how an edge is defined. This superposition of equally true states is what creates the world.
@lyn8964
2 жыл бұрын
thank you very much, from a german uni student :)
@vizziiiiob
Жыл бұрын
What should I know before getting into graph theory?
@nazifataha8868
4 жыл бұрын
you are absolutely amazing ! Thank you
@hchen31
2 жыл бұрын
Does path have to be the shortest walk? 26:28 Can path be: b -> a -> c -> d (no repeated vertices, but not the shortest walk)? Thank you!
@quirkyquester
6 жыл бұрын
This is sooo great ! Thank you so much!!!
@prencesschricelgaray8011
4 жыл бұрын
Thank you so much. This is very helpful.😊❤️
@adristimaulidafauzi4418
4 жыл бұрын
this literally better than 2 hours wasting my time in class and learn nothing
@marjoqako7887
3 жыл бұрын
same here
@reemhesham5918
3 жыл бұрын
this video helped me so much... thank youu
@moayyadarz2965
4 жыл бұрын
thank you .. it is a bery good way of explaining such of complex concepts in very simple way
@moayyadarz2965
4 жыл бұрын
but I have a question about the terms what do you exactly mean by saying ********(v choose 2)=(v .(v-1 ) / 2! ) so my question how do you solve in this way what is the rule that controls the way thanks in advanced
@rymlallaouh2574
2 жыл бұрын
Thanks from Algeria ❤️✌️
@joshuaomotosho7463
6 ай бұрын
You are a great tutor How did you get e choose v2
@DOMINANTbeats
5 жыл бұрын
Proof attempt at 24:00 mark: Suppose there does not exist a path in any x-y walk. Suppose we have w to be a minimal walk from x to y. Easy Case: If there is no repeated vertex, then by definition there is a path. Other Case: Assume any of those edges connects x to y must have repeated vertices. Each edge must then go back to a certain vertices more than once, where we note that a minimal walk does not repeat a path. Therefore a contradiction.
@rayanalqudsi5486
10 ай бұрын
what a legend
@antonheimdal8445
3 жыл бұрын
For the dense people who are having a bit of a difficult time finding the solution to the last problem. Is there any answer somewhere. Step by step explanations on solving these sort of problems, both simple and complicated ones. I am feeling frustrated with this topic since I can't seem to get the application of it. I understand why and how but proofing mathematically is something I have struggled in Graph Theory. Help someone!
@Legendofmudkip
8 жыл бұрын
My professor taught us that (at 4:52) if there is an arrow going in one direction, then it is an undirected graph. So a to b would be undirected. And if there is a set of two arrows going in opposite directions from the same point, then that is a directed graph. So a to c would be a directed graph.
@Trevtutor
8 жыл бұрын
+xdarkness22x If there are arrow heads, it's directed. If there are no arrow heads, it's undirected. This is standard convention. For the sake of your course, it might be a little different.
@Legendofmudkip
8 жыл бұрын
TheTrevTutor Eh, my professor is probably teaching us wrong material. It wouldnt be the first time. Which is why I am every so grateful for your videos
@sperera5916
8 жыл бұрын
You are really great! I understand things clearly. I have subscribed you.
@souritraghosh1054
3 жыл бұрын
Thank you sir.... Hopefully I will take a good exam tomorrow.
@jerrickmarques8777
5 жыл бұрын
That's some great mouse control. Your mouse-writing looks better than my handwriting
@johntremendol
5 жыл бұрын
i doubt its a mouse. probably a light pen
@luisdfernandez2601
3 жыл бұрын
24:35 "A trail has repeated edges" but trails don't have repeated edges, correct?
@oguz-kagan
3 жыл бұрын
yes. i didn't understand that part. now both of them are not repeated?
@oguz-kagan
3 жыл бұрын
ah i get it. in trail you can repeat edge. in path you can't repeat vertex.
@NPOCrushader
4 жыл бұрын
Told my classmates about your channel, and these videos will help us immensely!!
@DanielAlmeida499
3 жыл бұрын
great video, thank you!
@ritsu7337
2 жыл бұрын
Um, for the last demonstration, I've resolved it as follows : We know that E (number of edges) has to be
@withtechguy7552
3 жыл бұрын
Very well explained sir..
@EDROCKSWOO
6 жыл бұрын
What does it mean for a vertex to have five neighbors. If i draw a vertex with five edges connecting with five other vertices, are those considered neighbors? Also, when I draw five neighborhoods does that satisfy condition two of this problem? Draw a graph that has 2) at least three vertices that are all adjacent to each other, and 3) a vertex with five neighbors.
@youngee9403
7 жыл бұрын
You sir are a life saver
@ace4x3
2 жыл бұрын
Very clear thank you
@rhysbroughton8869
2 жыл бұрын
you're a hero
@jordanschwartz6163
Жыл бұрын
To prove that for all x to y walks, there exists an x to y path, we can use a proof by contradiction. First, assume that there exists a walk, denoted as w, from x to y that is not a path. This means that w contains repeated vertices or edges, which makes it longer than the shortest possible path from x to y. Now, let's consider a minimal walk, denoted as w', from x to y. By definition, w' is the shortest walk from x to y. Since w is not a path, it must be longer than w'. Next, we will show that there exists an x to y path that is shorter than w. Consider the subsequence of w' that consists of only the distinct vertices. Since w' is a minimal walk, this subsequence is also a walk from x to y. Moreover, it is a path because it does not contain any repeated vertices. Since this subsequence is a path, it is shorter than w because it does not have any repeated vertices or edges. This contradicts our assumption that w is the shortest walk from x to y. Therefore, our assumption that there exists a walk that is not a path is false. Hence, for all x to y walks, there exists an x to y path.
@chexblu
2 жыл бұрын
where can I find hamiltonian? awesome video btw, thanks a lot
@themaps7166
6 жыл бұрын
Very helpful,thank you sir !
@anchanakrishnangp2086
3 жыл бұрын
Thank you sir Thanks a lot
@mariachiinajar
3 жыл бұрын
que pasión! crazy mathemagician! ❤️❤️❤️
@ritikyadav3470
3 жыл бұрын
I understand whole thing clearly . Niceeeee......... :)
@mihackerz4268
8 жыл бұрын
Sir the video was really good but i am having two doubts: 1. In first question is it possible to have a path which is not a trail if not can you u give one example. 2. v choose 2 is simply combination vC2 but it signifies nCr means n!/(r!(n-r)! then how you can write v(v-1)/2 simply. I didn't understand Please can someone help me out in this problem
@yahya9889
7 жыл бұрын
are you indian?
@mihackerz4268
7 жыл бұрын
Yaa
@TheAmbionC
7 жыл бұрын
vC2 = v! / (2! (v - 2)!) = v (v - 1) * (v - 2)! / (2 (v - 2)!) = v (v - 1) / 2
@gabrielvillegas2033
4 жыл бұрын
@18:00 that is quite the graphic graph
@sjoligames3687
3 жыл бұрын
Path b -> d, u use bcd. Thats also a trail? Dont u have to deny trail by using an edge twice before u can properly call it a path?
@itsmeyaw_id
5 жыл бұрын
Hello, I just want to tell that maybe there is a mistake in the video. As I read, simple path means that there isn't any multiple verticies instead of edges. Anyway, thanks for the lesson. I can understand graph theory better now.
@markkennedy9767
3 жыл бұрын
At 18:50 how do loops affect connectivity. If you go between say a and a, is this a path since a is used twice (so a is not connected to itself? Or do we accept cycles (closed paths) here as ways of connecting a to a). Or do we only take paths between vertices where x!=y to deal with this.
@johndouros3759
4 жыл бұрын
Im dreading this so much
@jeantortuga570
5 жыл бұрын
why choose 2? Is 2 meant as a number of vertices that are connected with an edge?
@masumbillah3075
5 жыл бұрын
cause in a simple graph,we need two vertices to make an edge so,the number of ways by which we can get a pair of vertices,is equal to the maximum number of edges we can form with those vertices! the way of choosing 2vertices [pair of vertices] from N number of vertices is , NC2 ,so,maximum number of edges we can get is = NC2 so,number of edges
@pubgvlogger8913
3 жыл бұрын
Could you please send me answers sir in symbolic form❤️ (b) Susan sits between Tom and Bill. (c) x is the father of the mother of y. (d) All the world loves a lover
@aspkaushik
9 жыл бұрын
AWESOME!!!!! well done man. Terse and neat
@wcxjordan9859
8 жыл бұрын
+kasp HAHAHHA
@deehee1181
4 жыл бұрын
is it possible for you to go back and forth in a directed graph?
@LorddGray
8 жыл бұрын
If vertex has a single edge that just goes to itself, is it still "isolated"?
@Trevtutor
8 жыл бұрын
by definition, no, since it doesn't have degree = 0.
@kama8213
4 жыл бұрын
Holy shiiiit, maximum thanks to this person!
@Lrdnqustr
Жыл бұрын
What's "V choose 2"? Is that permutations? Combinations? I'm sorry for being stupid...
@farscamidediniz
5 жыл бұрын
Thank you soo much
@ragn594
2 жыл бұрын
Can I please get an explination as to what the 2 is in the last example/exercise. I don't understand what this 2 does is it the amount of connections that every vertex has? What is the meaning of it?
@claxxicmedia6963
Жыл бұрын
Is it a must I repeat vertices to find Trail
@baldjaebeom4424
2 жыл бұрын
i skipped my lectures bc online classes are meh,, thanks for mansplaining this to me xx
@hisabin
5 жыл бұрын
Thank you sir
@RepeaterCreeper
3 жыл бұрын
What software is that for drawing? Seems a little more convenient than SmoothDraw
@cybervigilante
3 жыл бұрын
Can you increase the number of possible trails by starting at a different vertex, or does the number always remain the same? I think it's the latter, but I don't have a proof.
@kenriccrasta8603
2 жыл бұрын
can we go back and forth in walks for directed graphs
@mustafamustafammrr
7 жыл бұрын
u r soo good
@sophiaabssi3173
Жыл бұрын
Is an isolated vertex a simple path please ?
@yavuzkoca8352
8 жыл бұрын
Thanks a lot!
@jeandanielyannickchloe8149
2 жыл бұрын
Is there any book (pdf) i can used to work some exercise on graph please?
@aaronpaulbarsana1702
3 жыл бұрын
thank you :)
@ensaruslu409
6 жыл бұрын
really really thx man. u saved my life :D
@darkferiousity
Жыл бұрын
I laughed quite a bit when you drew a vector
@gabrielcastillo6907
7 жыл бұрын
Sir in the last exercise. Where did you get the formula v(v-1)/2!
@anibalc.ripollr.9643
7 жыл бұрын
Note that C(V,2)= V! / 2! (V-2)! = V(V-1)(V-2)! / 2 (V-2)!, cancel out the term (V-2)! on the numerator and the denominator and you get V(V-1) / 2
@keithramanjooloo7464
3 жыл бұрын
God bless you my g
@davidhand9721
Ай бұрын
The different meanings of path, trail, walk etc. are like abuse of notarion in English. I feel like I'm justified in calling this set of definitions _bad_ in an objective sense. These should all be _properties_ of a single object that can be referred to by any of those names because they all mean the same thing.
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