Iranian Journal of

Let T be a tree and n_{l}(eIT) and n_{2}(eIT) denote the number of vertices of T, lying on the two sides of the edge e. Suppose T_{l} and T_{2} are two trees with equal number of vertices, e in T_{1} and f in T_{2}. The edges e and f are said to be equiseparable if either n_{l}(eIT_{I}) = n_{l}(fIT_{2}) or n_{l}(eIT_{I}) = n_{2}(fIT_{2}). If there is an one-to-one correspondence between the vertices of T_{l} and T_{2} such that the corresponding edges are equisep arable, then T_{ }and T_{2} 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.

Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new algorithm for computing the detour index of molecular graphs is presented. We apply our algorithm on copper and silver nanoclusters to find their detour index.

In this paper, two methods are described, by means of which it is possible to calculate the non rigid group of molecules consisting of a number of XH3 groups attached to a rigid framework. The first method is a combination of the wreath product formalism of Balasubramanian and modern computer algebra and the second method is a computational approach by using group theory package GAP. We apply these methods on 2,3,6,7,10,11-hexanitrotriphenylene (HNT) to compute its non-rigid group.