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 $h$.