The cyclic graph

A cyclic graph of order , , is a connected graph with vertices in which every vertex has degree 2.

Equivalently we can define it as a graph with vertices that can be ordered as so that the set of edges is the set with and or and .

The condition is due to the fact that we don't have multiple edges or loops.


This is the cyclic graph with 7 vertices.

In GrInvIn you can create a cyclic graph by using the cyclic graph factory.

Properties

The cyclic graph of order is

These are some invariant values for the cyclic graph of order :

Invariant nameInvariant value
Size
Diameter when is even
when is odd
Girth
Clique number3, when
2 in all other cases