What is the Difference Between Walk and Path?
🆚 Go to Comparative Table 🆚The main differences between walks and paths in graph theory are as follows:
- Walk: A walk consists of an alternating sequence of vertices and edges, where consecutive elements are incident, and it begins and ends with a vertex. Walks can have repeated vertices and edges. A walk is an open walk if the starting and ending vertices are different, and it is a closed walk if the starting and ending vertices are the same.
- Path: A path is a walk without repeated vertices. It is also an open walk, meaning it does not repeat a vertex or an edge. A path with no repeated edges is called a trail. A path is equivalent to a trail with no repeated vertices.
In summary:
- Walks can have repeated vertices and edges, and they can be open or closed.
- Paths do not repeat vertices, and they can be open.
- Trails do not repeat edges, and they are open walks.
Comparative Table: Walk vs Path
The difference between a walk and a path can be summarized as follows:
Walk | Path |
---|---|
A walk is a finite sequence of alternating vertices and edges, where each edge's endpoints are the two vertices adjacent to it. | A path is a walk in which all vertices are distinct, meaning no vertex is repeated. |
A walk can be open (first and last vertex are not equal) or closed (first and last vertex are equal). | A path is always simple, meaning it does not repeat any vertices. |
A walk may contain repeated edges. | A path does not repeat any edges. |
In a walk, vertices and edges may be traversed multiple times. | In a path, vertices are visited only once, but edges may be traversed multiple times. |
In graph theory, a walk is a sequence of edges and vertices, while a path is a specific type of walk where all vertices are distinct and visited only once.
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