doiSerbia

Equiseparable chemical trees

Gutman Ivan (Faculty ov Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac)
Arsić Biljana (Faculty of Science, University of Niš, Niš, Serbia and Montenegro)
Furtula Boris (Faculty ov Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac)

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. Let T1 and T2 be two trees with equal number of vertices, let e be an edge of T1 and f an edge of T2. Then e and f are said to be equiseparable 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 T2 are equiseparable trees. A number 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. .

Keywords: Wiener index, variable Wiener index, chemical trees, alkanes, equiseparability