مرکز منطقه ای اطلاع رساني علوم و فناوري -

چكيده لاتين :

Let T be a tree and n1(eIT) and n2(eIT) denote the number of vertices of T, lying on the two sides of the edge e. Suppose T1 and T2 are two trees with equal number of vertices, e element T1 and f element T2. The edges e and f are said to be equiseparable if either n1(eIT1) = n1(fIT2) or n1(eIT1) = n2(fIT2). If there is an one-to-one correspondence between the vertices of T1 and T2 such that the corresponding edges are equisep arable, then T and T2 are called equiseparable trees. Recently, Gutman, Arsic and Furtula investigated some equiseparable alkanes and obtained some useful rules (see J. Serb. Chem. Soc. (68)7 (2003), 549-555). In this paper, we use a combinatorial argument to find an equivalent def inition for equiseparability and then prove some results about relation of equiseparability and isomorphism of trees. We also obtain an exact expression for the number of distinct alkanes on n vertices which three of them has degree one.