Cycle graph - Definition and Overview

In the mathematical field of graph theory a cycle graph or circle graph is a graph that consists of a cycle. The circle graph with <math>n<math> vertices is called <math>C_n<math>.

A directed cycle graph or a dicycle graph is a diconnected cycle graph, that is all directed edges in the cycle point in the same direction.

Properties

• A circle graph is
• connected
• 2-regular.
• Eulerian.
• Hamiltonian.
• symmetric.

• 2-vertex colorable and 2-edge colorable if it has an even number vertices.
• 3-vertex colorable and 3-edge colorable if it has an odd number of vertices.

References

• Eric W. Weisstein, Cycle Graph (http://mathworld.wolfram.com/CycleGraph.html) at MathWorld.