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The subtrees and BC-subtrees (subtrees where any two leaves are at evendistance apart) have been extensively studied in recent years. Such structures,under special constraints on degrees, have applications in many fields. Throughan approach based on generating functions, we present recursive algorithms forenumerating various subtrees and BC-subtrees of maximum degree $\leq k$ intrees. The algorithms are illustrated through detailed examples. We alsobriefly discuss, in trees, the densities of subtrees (resp.~BC-subtrees) ofmaximum degree $\leq k(\geq 2)$ among all subtrees (resp.~BC-subtrees).

Subtrees and BC-subtrees of maximum degree no more than k in trees