Cage

Definition

Suppose $d$ and $g$ are positive integers, with $g\ge 3$. Consider the collection of all finite undirected graphs that are $d$-regular graphs and have girth $g$. A $(d,g)$-cage is a graph in this collection that has the minimum possible number of vertices, i.e., there is no graph in the collection with fewer vertices.

If $d$ is not explicitly specified, then we are referring to the case $d=3$, i.e., to cubic graphs.