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

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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

[@DJGamimg627]

I guess path circuit ho ya kuch aur wo sab walk ho saktay hai agar may galat hu toh pls correct me 😅

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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

[@Brar_entertainment]

@@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

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(c) 2 & 3 ✅

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Sir is the answer 1.c and 2.d

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[@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.

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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

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Q-2 option D is correct

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1. C 2. B

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Option (C) 2 and 3

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

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

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[@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.

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Q1 : C ans Q2 : d ans

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

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Q1 C)2 and 3

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