What is the difference between Walk, Trial, Path, Circuit and Cycle ?

What is the difference between Walk, Trial, Path, Circuit and Cycle ?

  Walk - It is defined as the the sequence of alternating vertices and edges in a graph.

   while travelling in a walk,  the vertices and edges can be repeated.

 It is not compulsory that we should travel all the the edges and vertices.  So the length of the

 walk is equal to the number of edges travelled.

Trail -  trial  is also a walk but no edges repeated.

 Remember, vertex can be repeated

 

 Path -  In a path either vertex and edges should not be repeated.

Circuit - Circuit is also like a trail because vertices must not be repeated.  But

 difference between a circuit and trial is a circuit must have  the start and the end vertex same.

Cycle - cycle is a closed path in which the vertices and edges must not be repeated.

 Edges should not be repeated.

 Vertices should not be repeated (except the start and end vertices)

CHART FOR EASY UNDERSTANDING :

R - Can be Repeated
NR - No Repeation.