On BC-trees and BC-subtrees

A BC-tree (block-cutpoint-tree) is a tree (with at least two vertices) where the distance between any two leaves is even. Motivated from the study of the “core” of a graph, BC-trees provide an interesting class of trees. We consider questions related to BC-trees as an effort to make modest progress towards the understanding of this concept. Constructive algorithms are provided for BC-trees with given order and number of leaves whenever possible. The concept of BC-subtrees is naturally introduced. Inspired by analogous work on trees and subtrees, we also present some extremal results and briefly discuss the “middle part” of a tree with respect to the number of BC-subtrees.