**Circuits**

A **circuit** is a sequence of edges linking successive vertices that starts and finishes at the same vertex.

*Essential Further Mathematics 4ed 2012 (Fig 23.9)*

**Possible Circuits: **

- A, B, C, D, F, A.
- E, F, D, E.

## Sub-Graph

A **sub-graph** is a graph that consists of selected edges and vertices of the graph with the same links as the original graphs and with selected vertices including all the endpoints of the selected graph.

Using the above example (Fig 23.9), the following diagrams below are sub-graphs of that graph.

*Essential Further Mathematics 4ed 2012 (Fig 23.10a&b)*

*The sub-graph is shown as red lines.

*Essential Further Mathematics 4ed 2012 (Fig 23.10c)*

Fig 23.10c is NOT a sub-graph, because it contains an edge that is not present in the original graph (Fig 23.9)

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