Equiseparable chemical trees

Abstract

Let n1(e|T) and n2(e|T) denote the number of vertices of a tree T, lying on the two sides of the edge e.LetT1and T2be two trees with equal number of vertices, let ebe an edge of T1andfanedgeofT2.Theneandfaresaidtobeequiseparable if either n1(e|T1)=n1(f|T2) or n1(e|T1)=n2(f|T2). If all edges of T1 and T2 can be chosen so as to form equiseparable pairs, then T1 and T2are equiseparable trees. Anumber of molecular structure-descriptors of equiseparable chemical trees coincide, implying that the corresponding alkane isomers must have similar physico-chemical properties. It is shown how equiseparable chemical trees can be constructed in a systematic manner.