The test differs whether the tree is rooted or not. An urooted tree is
considered binary if all its nodes are of degree three (i.e., three
edges connect to each node). A rooted tree is considered binary if all
nodes (including the root node) have exactly two descendant nodes, so
that they are of degree three expect the root which is of degree 2.
is.binary.tree is deprecated and will be removed soon:
currently it calls is.binary.