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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 verticies 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 <math>K_m<math> is strongly regular for any <math>m<math>.
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