Families of equiseparable trees and chemical trees

Abstract

Let T be an n-vertex tree and e its edge. By n1(e|T) and n2(e|T) are denoted the number of vertices of T lying on the two sides of e; n1(e|T} + n2(e|T) = n. Conventionally, n1(e|T) ≤ n2(e|T). If T' and T" are two trees with the same number n of vertices, and if their edges e'1, e'2,..., e'n-1 and e"1,e"2,...,6"n-1 can be labeled so that n1(e'i|T') =n1(e"i|T") holds for all i = 1,2,...,n- 1, then T' and T" are said to be equi-separable. There exist large families of equiseparable trees. We report here the results of a systematic study of these families for 7 ≤ n ≤ 20.