What is the degree of a tree? (As in, a tree ADT)

Question

I understand that the degree of a node is the number of children it has.

However, how do we define the degree of a tree?

Answer 1

Every node is itself a tree. The degree of a tree is the degree of the root node.

Answer 2

For a rooted tree you might define it as the degree of the root. In some scenarios saying it is the maximum degree of any node in the tree might make sense. But without context it is hard to say what the right definition is. It depends on how you want to use it and what is significant about the "degree" of a tree. If you have a concrete example in mind, or a piece of text that you find puzzling, please update the question.

Answer 3

In general a graph has a minimum degree and a maximum degree, that is just the minimum respectivly the maximum degree of all nodes in the graph.

If a graph is k-regular, that is all nodes have exactly k neighbours, minimum and maximum degree equal k and the graph is said to be of degree k.

Because a tree is not k-regular you cannot say it has grad k, but you can find its minimum or maximum grad.

Quite common are k-ary trees, that are rooted trees where each node has at most k childs.