Circulant graph

In graph theory, a circulant graph is an undirected graph that has a cyclic group of symmetries that includes a symmetry taking any vertex to any other vertex.

Equivalent definitions

Circulant graphs can be described in several equivalent ways:

Examples

Every cycle graph is a circulant graph, as is every crown graph with 2 modulo 4 vertices.

The Paley graphs of order n (where n is a prime number congruent to 1 modulo 4) is a graph in which the vertices are the numbers from 0 to n − 1 and two vertices are adjacent if their difference is a quadratic residue modulo n. Since the presence or absence of an edge depends only on the difference modulo n of two vertex numbers, any Paley graph is a circulant graph.