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Paths and cycles

Maths Applications (Year 12) - Graphs and Networks

Bhakti Sharma

Paths and Cycles

As mentioned before, a walk is a sequence of vertices in which each vertex point is joined to the next by an edge. A path is a walk that doesn’t involve any repeated use of edges and vertices, except for potentially ending up at the same vertex from which the path started. An open path is one that starts and finishes at different vertices, whereas a closed path (or cycle), is one that starts and ends at the same vertex.


An example of an open path is as follows:

As you can see, the path starts and finishes at the letter A, however, does not repeat the use of any vertices or edges. Now, let’s look at an example of a closed path:



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