Graph Theory

Question

1. Walk    : Vertices may repeat. Edges may repeat (Closed or Open)
2. Trail     : Vertices may repeat. Edges cannot repeat (Open)
3. Circuit : Vertices may repeat. Edges cannot repeat (Closed)
4. Path     : Vertices cannot repeat. Edges cannot repeat (Open)
5. Cycle    : Vertices cannot repeat. Edges cannot repeat (Closed)

Can someone verify these terminologies? They are pretty confusing :/

Comments

1. no edge appears more than once

2. Same as walk

3. yes corrct

4.yes corrct as u described

5.closed walk , no vertices appears more than once, except starting and ending only

---

I found a definition at the below link about walk and trail

A walk consists of an alternating sequence of vertices and edges consecutive elements of which are incident, that begins and ends with a vertex. A trail is a walk without repeated edges. A path is a walk without repeated vertices.

Ref: https://www.di.ens.fr/~zhentao/math363/introGRAPHS.pdf

---

definitions depend on which author you are following because walk have 2 definitions in one, vertices and edges can be repeated and in narsingh deo edges cannot be repeated. Moving on, Path is non-intersecting open walk and circuit is non-intersecting closed walk.

Walk is also referred as chain or edge train because non-retracing sequence of edges.

Cycle graphs have only one circuit and they have same number of edges and vertices.

Cycle graphs are different from cyclic graph.

Cyclic graphs are those graphs which consist at-least 1 circuit but cycle graph consist circuit with size same as number of edges.

Trail is not important terminology but still it is a walk with no repeated edges.

---

Correct me if I am wrong!

Answer 1

The definitions are correct but they are not hard and fast, and can vary in some questions.

Ref: 

https://math.stackexchange.com/questions/655589/what-is-difference-between-cycle-path-and-circuit-in-graph-theory

https://www.quora.com/What-is-the-difference-between-a-walk-and-a-path-in-graph-theory