Across two different texts, I have seen two different definitions of a leaf
1) a leaf is a node in a tree with degree 1
2) a leaf is a node in a tree with no children
The problem that I see with def #2 is that if the graph is not rooted, it might not be clear whether a node, n, has adjacent nodes that are its children or its parents
So is it just always safer to go with def #1? Or is def #2 restricted to rooted trees? Why do some authors present these definition differently?