INTRODUCTION to GRAPH THEORY - DISCRETE MATHEMATICS

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We introduce a bunch of terms in graph theory like edge, vertex, trail, walk, and path.

#DiscreteMath #Mathematics #GraphTheory

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Introduction to Graph Theory. We cover a lot of definitions today, specifically walks, closed walks, paths, cycles, trails, circuits, adjacency, incidence, isolated vertices, and more.

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I am seeing this video after 5 years (2021) . For my semister exams, you explained very clearly . Thank you man

anisivaram
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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.

jackmenirons
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On my final stretch with discrete maths. Thank you sir. for all you have done, God bles!

bestyoueverhad.
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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 <3

hats
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6:38 Walk
10:09 Trail & Circuit
13:23 Path & Cycle
24:27

kaizen
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In just few minutes and I understand this better than my maths teacher..thank you

vitalispurity
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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.

beccalynn
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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

tolulopevictor
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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...

alizesavim
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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.

evanknowles
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I watched these video's after six years . You tought in a very understandable manner thank you so much.

giridharkrcomputerscience
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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

NewtonCazzaro
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Im getting ready to start descrete mathematics next tuesday for university and your videos are very helpful.

dc.gamedesigner
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8 isolated vertices disliked this video.

sperera
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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! :)

haukwantung
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For reviewing purpose, and got an A in direcrete math. Thank you so much!

levyax
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one of the best tutorial I have ever watched on youtube

kanchapagimhara
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For the question asked for all walk there exists a
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

AbhishekTiwarics
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Thank you man. You are such a brilliant teacher!

proggenius
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Thanks man, read Lecture notes and bamboozled myself . But this helped

xiaoraven