Biregular graph

In graph-theoretic mathematics, a biregular graph or semiregular bipartite graph is a bipartite graph $G=(U,V,E)$ for which every two vertices on the same side of the given bipartition have the same degree as each other. If the degree of the vertices in $U$ is $x$ and the degree of the vertices in $V$ is $y$ , then the graph is said to be $(x,y)$ -biregular.

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