Final answer:
The maximum degree of a tree with exactly 2 leaves and more than 2 nodes depends on the way nodes are connected and hence, depends on the number of nodes in the tree.
Step-by-step explanation:
In graph theory and discrete mathematics, a tree is a special kind of graph that does not contain any cycles and is connected. Trees are often characterized by their nodes and edges, where leaves are nodes with a degree of one. From the question, it is clear that we have a tree structure with exactly 2 leaves and more than 2 nodes. The question asks us for the maximum degree of the tree.
The degree of a node is the number of edges incident to it. Since a tree with exactly 2 leaves is given, and there are more than 2 nodes (n>2), the tree must have at least one node, called an internal node, which connects multiple other nodes. Therefore, the maximum degree of the tree depends on how these internal nodes are connected. Given that we are dealing with a simple tree (a connected acyclic graph), the maximum degree will be determined by the node with the highest number of connections to other nodes.
For example, if we imagine a tree with 5 nodes, and consider it to be a star-like structure where one central node is connected directly with the other four nodes, then this central node will have a degree of 4. Hence, the maximum degree of the tree in such a case is 4. This can vary based on the structure of the tree but will always be dependent on the number of nodes in the tree. Consequently, the correct answer to the question is B. depends on the number of nodes in the tree.