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

Published: 08 February 2019
on channel: Gate Smashers

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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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