Cycle Graphs
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Cycle Graphs

Definition: A graph $G = (V(G), E(G))$ is said to be a Cycle Graph if it consists only of a single cycle of vertices and edges. That is, the entire graph is a cycle.

We denote cycle graphs by $C_n$ where $n$ represents the number of vertices of the cycle graph. The cycle graphs $C_4$, $C_5$, and $C_6$ are shown below:


Notice that all cycle graphs for $n \geq 3$ can be drawn a regular polygons, for example triangles ($C_3$), squares, parallelograms, and rhombuses ($C_4$), pentagons ($C_5$), etc…

It is also important to note that cycle graphs all have degree $2$, and each cycle has exactly $n$-edges by The Handshaking Lemma.

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