Journal of the Serbian Chemical Society 2003 Volume 68, Issue 7, Pages: 549-555
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Equiseparable chemical trees
Gutman Ivan, Arsić Biljana, Furtula Boris
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