In graph theory, a regular graph is a graph where each vertex has the same number of neighbors. A regular graph with vertices of valency k is called a k-regular graph.

Regular graph of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of disconnected cycles.

A 3-regular graph is know as a cubic graph.

A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices.

The complete graph K_m is strongly regular for any m.

References

• Eric W. Weisstein, Strongly Regular Graph at MathWorld.