m-ary Tree

When all internal vertices has $\le m$ children.

Full m-ary tree

When all internal vertices have exactly $m$ children.

A full $m$-ary tree with:

• $n$ vertices has $i = (n-1)/m$ internal vertices and $l = [(m-1)n + 1]/m$ leaves.
• $i$ internal vertices has $n = mi + 1$ vertices and $l = (m-1)i + 1$ leaves.
• $l$ leaves has $n = (ml-1)/(m-1)$ vertices and $i = (l-1)/(m-1)$ internal vertices.

There are at most $m^h$ leaves in an $m$-ary tree of height $h$.