Regular tree
= Regular tree
{title2=$\deg(x)=k\quad(x\in V)$}
An infinite connected <tree> is regular of degree $k$ if every <vertex> has exactly $k$ neighbours. Necessarily $k\ge2$. For $k=2$ it is a two-sided infinite path. For $k\ge3$, rooting it gives $k$ children at the root and $k-1$ children at each other <vertex>; this constructs the unique such tree up to <graph isomorphism>.