Difference between Walk, Trail, Path, Circuit and Cycle with most suitable example | Graph Theory

#graphTheory#trail#circuit#cycle#intel
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1. Walk - A walk is a sequence of vertices and edges of a graph i.e. if we traverse a graph then we get a walk.
2. Trail - Trail is an open walk in which no edge is repeated.
3. Path - It is a trail in which neither vertices nor edges are repeated i.e. if we traverse a graph such that we do not repeat a vertex and nor we repeat an edge. As path is also a trail, thus it is also an open walk.
4. Circuit - Traversing a graph such that not an edge is repeated but vertex can be repeated and it is closed also i.e. it is a closed trail.
5. Cycle - Traversing a graph such that we do not repeat a vertex nor we repeat a edge but the starting and ending vertex must be same i.e. we can repeat starting and ending vertex only then we get a cycle.
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[@himanshumaurya2496]

Option C is correct i.e. 2 and 3 ( 2. A TRAIL is always a walk and 3. A PATH is always a walk. )

[@simpleperson404]

because WALK is superset so other two options eliminated ez

[@shubhpatkar862]

yes exactly, option C is correct

[@sp8976]

@@shubhpatkar862 no because in walk verteces and edges repetation are allowed

[@amarnathprajapati2543]

Q1- c
Q2-d
Thanks Sir, Your videos are very helpful for me.

[@sahilkadecha9831]

correct nath

[@Mad_Reaper]

So 1(C) & 2(D)??
Also aweomse video, ik its been 4 years but its still helping so many students.
Keep up the great work sir!🔥

[@ansmehmood9415]

i think 2 (A) bcz edges and vertex are available

[@sahilprasantachoudhury911]

Self referential note:
Walk : Vertex✓, Edge ✓
Trail : Vertex✓, Edge × ; Closed Trail aka Circuit
Path : Vertex × (Except 1st and last Vertex) ; Closed Path aka Cycle

[@basitrahman514]

What about repeating the edges in Path ?

[@ayyappapalani288]

@@basitrahman514 edges shouldn't be repeated in path

[@deenkibatain754]

Vertices should not repeat

[@cartoons__for__kids_Hindi]

@@basitrahman514 when you can't repeat a vertex, then you naturally cannot repeat a edge, if you try to repeat a edge, a vertex will get repeated

[@basitrahman514]

@@cartoons__for__kids_Hindi thanks..got it

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[@garimasrivastava2952]

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[@insatgaming2932]

BCA ?

[@nabilaali8548]

Exactly

[@ankandebnath1056]

Q1) (C) 2 and 3
2) A trail is a walk
3) A path is walk
Q2) (D) a->f->b->g->e->b->a is a circuit but not path
As b vertex is repeated.

[@fasana1110]

2 (a) is not correct?

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[@abdulqudoos6824]

asey desi zubaan main lecture sunnay ka mzah he kuch aur hai qasam say thankyou sir

[@alayamaryim]

Q1. C
Q2. D
Nice delivery👍

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Simple and best explanation ❤️❤️❤️❤️

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Sir aapki samjhane ki technique bahut achi ha ekdm se concepts clear jo haate ha

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हर हर महादेव जय माँ भवानी जय श्रीराम जय माँ सीता जय हनुमानजी हर हर महादेव जय माँ भवानी जय श्रीराम जय माँ सीता जय हनुमानजी 🙏🙏🙏🙏🙏🙏❤❤❤❤❤❤🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩

[@shivkumartaneja]

Very nice explanation 👌

[@jinip451]

Sir is the answer 1.c and 2.d

[@memeworld91919]

Thank u guru ji

[@madhurjyadeka5569]

Q1 option c.. by using set theory Trails and paths will always be inside the Walk set

[@abhishekgaurav9908]

Yeah its correct.

[@88_avinashprakashsherla82]

Thank you sir ji❤

[@chiki6704]

You teach really well sir Respect++
and your Punjabi accent is sweet to hear 😁

[@ramanrajagopalan3215]

Hi this is my observation correct me if am wrong Q1: Walk is a bigger entity and trail and path are sub entities under walk. So option1 Walk is always a trail Yes!! , option2 and 3 NO!!. At last option4 Walk is always a path. So we can conclude by saying that B is the right answer.

[@aerbhamukesh7273]

Bahot badiya ...
Easy explanation...
Thank you...
Keep it up...

[@Anirudh_Srinivasan]

C) 2 and 3 is the right answer.

[@seemapp3951]

1-2 and 3 right
2-1--walk but not trail
2--trail and also close path
3--circuit and cycle both
4--its path but not circuit

[@SanglapKundu]

1.c 2. D
Thank u sir 🙂

[@jasdeepsingh7553]

Option c of 1st question and d of 2nd question

[@shaifali3105]

Bohot ache explain kar rahe ho sir.... Awesome

[@rutujamohite4434]

Amazing 👍

[@muhammadi8141]

Q1- c)
Q2- d) is a circuit but not path because vertex 'b' is repeated .

[@yashthakkar4549]

a to f to b and b to a are different edges?

[@SatvikaVyas]

The edge between b and a is repeating. Hence it is not a trail => not circuit

[@VivekKumar-jn5bb]

​@@SatvikaVyas ma'am kaha edges repeating ho rahi hai 🤔

[@CfffAszedc]

​@@SatvikaVyasThere is a parallel edge between a and b hence the edge is not repeating

[@hassaninbajwa7162]

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I appreciate your efforts

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so what are you doing now?

[@nomanriaz8134BhattiNotes]

Thanks sir,,,, am understand very easily and
It's Answers are
Q.1: c)
Q.2: d)

[@shivarajput1043]

Thanku Sir ji

[@mohitkumarmahata7525]

'C 2&3

[@sabbu3791]

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Life**

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[@prachiyargatti016]

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[@bibek6556]

Thank you very much sir
I have confused between them now it is clear for me

[@rounaknag68]

For Q2 option b shold be the answer as its not forming closed path also edges are not repeating so it should be trail

[@arslanhafeez2312]

Superb explanation

[@bhaveshbachhav6981]

Thanks sir, nice teaching all concept clear👍🏻.. 😇

[@syedghulamhassansherazi8028]

Correct Answer: © 2 and 3
Here’s why:
Statement 2: A trail is always a walk. This is true because a trail is a type of walk where no edge is repeated.
Statement 3: A path is always a walk. This is true because a path is a type of walk where no vertex is repeated.

[@vishalgarg3177]

1. C
2. B

[@PratimaYadav-bg3ug]

Thanku sir🙏

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thnkss alott ji...God bless u forever...

[@NeerajSharma-ug3ei]

good lectures .
que.1 c
que 2 d.

[@qurrat-ul-ain8331]

Nice explanation

[@Sonusonu-uc7is]

Q1 C)2 and 3

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Very nice sir

[@craftmedia3448]

9:14
Answer of the question is
C

[@rishabrajsoni8347]

Sir,can you make video related to path degree sequence and distance degree sequence

[@ramanrajagopalan3215]

Q2: option D) is right as the vertex b is repeated twice. Correct me if i am wrong

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Your learning method iss osm

[@atrikashow8118]

homework Answer---------------
< Q1 > ans -- c (2 & 3)
< Q2 > ans -- a (is a walk and also a trail).

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[@DEVILGAMING-kh1ue]

2 and 3 are correct

[@raghunandankrishnan6404]

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[@hinathanki3005]

Superb video...very useful

[@geethakc3562]

Ans is c)
Trail and Path are always a walk.
But walk can't be Trail and Path since V and E are repeated.

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[@shriyansh_agarwal]

Sir pls confirm the answers
Question 1- C (2 and 3)
Question 2- D (circuit but not path👣)

[@cartoons__for__kids_Hindi]

Right 👍

[@geetanjalibiswal7233]

Correct ans👍

[@jayminahir]

How i go b to a directly

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[@devang100]

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[@Sudeshsorout]

Very good sir g

[@mannbajpai4713]

1-c; 2-d THANK YOU SIR

[@theshow3734]

In question 2 c is also correct

[@hforheadshot6427]

Option (C) 2 and 3

[@LaxmanKumar-zu5vv]

Q1 - c
Q2- d. Because he ( B is repeated )

[@Allinone-fg1zt]

wonderful speech bro thnx

[@debjitroxx]

Q2 = option d(true)
b vertex is repeated so path is not possible but circuit is

[@preethamm.n1161]

Awesome explanation...!

[@ET-057]

hy .walk consist only vertex or egde....?

[@pujasumanthytripathy5366]

Thank you Sir🙏🙏🙏

[@deepikayadav9556]

Sir plzz continue co...

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Thanks sir

[@debashisbera]

1) -> option C is the ans
2) -> option D is the ans

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Thank u sir😊

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