--- ## Definition > [!tldr] Definition > For $n \geq 3$, The **cycle graph** on $n$ vertices is a graph which is simply a [[cycle]] of length $n$. That is, > - The vertex set is $V = \{1,2,\dots, n\}$. > - The edge set is the set $\{\{1,2\}, \{2,3\}, \{3,4\}, \dots, \{n-1, n\}, \{n,1\}\}$ Notes: - In $C_n$ the number of vertices and the number of edges is $n$. - Note that in the definition, $n \geq 3$. There is no such thing as $C_1$ or $C_2$. ## Examples and Non-Examples Here are visualizations of the cycle graphs $C_3$ through $C_6$: ![[cycle-grid.png]]