Regular graph

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other.^[1] A regular graph with vertices of degree $k$ is called a $k$ ‑regular graph or regular graph of degree $k$ .

^ Chen, Wai-Kai (1997). Graph Theory and its Engineering Applications. World Scientific. pp. 29. ISBN 978-981-02-1859-1.

[1] Chen, Wai-Kai (1997). Graph Theory and its Engineering Applications. World Scientific. pp. 29. ISBN 978-981-02-1859-1.

[1]

Graph families defined by their automorphisms
distance-transitive	→	distance-regular	←	strongly regular
↓
symmetric (arc-transitive)	←	t-transitive, $t \geq 2$		skew-symmetric
↓
_{(if connected)} vertex- and edge-transitive	→	edge-transitive and regular	→	edge-transitive
↓		↓		↓
vertex-transitive	→	regular	→	_{(if bipartite)} biregular
↑
Cayley graph	←	zero-symmetric		asymmetric