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

[@AbdulHadiEServices]

Amazing!!!! you are forcing me to press Like.

[@imranabbasi9535]

Never feel forced to do anything

[@iramkhan4798]

@@imranabbasi9535 hmm😁

[@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

[@garimasrivastava2952]

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You're an amazing teacher

[@insatgaming2932]

BCA ?

[@nabilaali8548]

Exactly

[@Tech_From_ground]

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[@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

[@akhileshchaudhary8821]

A 3 year old video means a lot to me!!

[@ankan.neutrinos]

Thanks sir for the guidence for syllebus and teaching so accurately from basic so that every student can learn ♥️

[@ruchika_7]

Cleared all my doubts..thankyou sir

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

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Your teaching method is the best ❤️

[@mr_roadhunter6603]

Thank you sir you are the best sir 🙏🙏🙏 thanks for always making us motivated and keep our studies up-to-date.

[@parvking5944]

Sir Hats Off 🛐🛐🛐 the way he explains makes its so easy to understand concept ekdum clear

[@aarohidua]

The topics which took hours for our uni lecturer to explain were explained so easily by you in the span of less than 10 mins each....forever grateful for this platform which helped me reach you sir

[@Allgaming-zw6et]

Hii

[@alayamaryim]

Q1. C
Q2. D
Nice delivery👍

[@anupamakumari2695]

Simple and best explanation ❤️❤️❤️❤️

[@JAISVEEN-spdn8]

Tq sir for uploading this amazing video 🎉❤🎉🎉

[@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

[@jinip451]

Sir is the answer 1.c and 2.d

[@ShivamGupta-by7vg]

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

[@Natural.168]

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THANKYOUSOOMUCH sir @

[@memeworld91919]

Thank u guru ji

[@divyrajverma8286]

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 🙏🙏🙏🙏🙏🙏❤❤❤❤❤❤🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩

[@jasdeepsingh7553]

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

[@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?

[@SanglapKundu]

1.c 2. D
Thank u sir 🙂

[@Anirudh_Srinivasan]

C) 2 and 3 is the right answer.

[@RUSHIPANSARE]

badiya sirrrrrrrrrrrrrrrrr

[@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.

[@madhurjyadeka5569]

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

[@abhishekgaurav9908]

Yeah its correct.

[@chiki6704]

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and your Punjabi accent is sweet to hear 😁

[@Atifrahman544]

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[@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

[@shaifali3105]

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

[@shivarajput1043]

Thanku Sir ji

[@88_avinashprakashsherla82]

Thank you sir ji❤

[@aerbhamukesh7273]

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

[@hassaninbajwa7162]

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I appreciate your efforts

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Very nice explanation 👌

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Life**

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Thanku sir🙏

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[@arslanhafeez2312]

Superb explanation

[@bibek6556]

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

[@BWU_BCA__Payel]

thanks sir
very helful video for the ugc students

[@mohitkumarmahata7525]

'C 2&3

[@prachiyargatti016]

You are so amazing sir

[@vishalgarg3177]

1. C
2. B

[@debarkiaravind5663]

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[@rutujamohite4434]

Amazing 👍

[@adityamishra8296]

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[@mannbajpai4713]

1-c; 2-d THANK YOU SIR

[@nomanriaz8134BhattiNotes]

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

[@kunalsingh5794]

Sir your videos are so helpful...👍👍👍👍

[@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

[@good114]

Thank you Sir 🙏🙏🙏🙏❤️❤️❤️

[@renulohan9535]

Q1 : C ans
Q2 : d ans

[@ramanrajagopalan3215]

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

[@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.

[@Sonusonu-uc7is]

Q1 C)2 and 3

[@NeerajSharma-ug3ei]

good lectures .
que.1 c
que 2 d.

[@abdullahanwar8064]

yours way of teaching was awesome really

[@anjalihagargi3707]

Sir net schedule k hisab se video start kijiye sir please

[@qurrat-ul-ain8331]

Nice explanation

[@mamatha6811]

Q1=C, Q2=D

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Your learning method iss osm

[@aswanikumarnayak4801]

❤❤

[@ssumida4531]

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[@hforheadshot6427]

Option (C) 2 and 3

[@vanshikashrivastav4962]

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[@devang100]

thank you sir

[@DEVILGAMING-kh1ue]

2 and 3 are correct

[@lecturesofilyas5136]

Best wishes from Pakistan

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[@deepikayadav9556]

Sir plzz continue co...

[@psychris_]

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[@ridasaif8757]

1-c,2-d

[@SanskarMishra-o2q]

Very nice sir

[@anshuman3652]

Thanks sir💞

[@debjitroxx]

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

[@rounak3239]

Gurujee shandhar jabardast zindabad

[@atrikashow8118]

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

[@shaliniyadav2996]

2 and 3 both correct in a
In q2 b is ans

[@hinathanki3005]

Superb video...very useful

[@rishabrajsoni8347]

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

[@LaxmanKumar-zu5vv]

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

[@ET-057]

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

[@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

[@CommonStudentActivity]

Option c is correct?

[@ਕਿਰਨਦੀਪਕੌਰ-ਠ8ਙ]

Thanks sir

[@raghunandankrishnan6404]

Bale bale shabha shabha understood sir

[@ginianto7515]

Thank u sir😊