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.
The cyclic graph of order is
These are some invariant values for the cyclic graph of order :
Invariant name | Invariant value |
---|---|
Size | |
Diameter | when is even when is odd |
Girth | |
Clique number | 3, when 2 in all other cases |