On Major and Minor Branches of Rooted Trees

Abstract

Let denote a rooted tree with n nodes. (For definitions not given here, see, e.g. [4]). For any node v of , let B(v) denote the subtree of determined by v and all nodes u such that v is between u and the root of ; node v serves as the root of B(v). The branches of are the subtrees B(v) such that node v is joined to the root of . A branch B with i nodes is a primary branch of if n/2 ≦ i ≦ n – 1; if has a primary branch B with i nodes, then a branch C with j nodes is a secondary branch if (n – i)/2 ≦ j ≦ n – 1 ≦ i; if has a primary branch B with i nodes and a secondary branch C with j nodes, then a branch D with h nodes is a tertiary branch if