Shell-polynomials and cluj-tehran index in tori t(4,4)s[5,n].

Weighted Hosoya polynomials have been developed by Diudea, in ref. Studia Univ. "Babes-Bolyai", 2002, 47, 131-139. Among various weighting schemes, those polynomials obtained by using Diudea's Shell matrix operator are far more interesting. We present here the Shell-Distance and Shell-Degree-Distance polynomials and close formulas to calculate them and derived Cluj-Tehran CT index in the family of square tiled tori T(4,4)S[5,n]. Applications of the proposed descriptors are also presented.

Symmetry properties of tetraammine platinum(II) with C2v and C4v point groups.

Let G be a weighted graph with adjacency matrix A=[a(ij)]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[d(ij)], where for i not = j, d(ij) is the Euclidean distance between the nuclei i and j. In this matrix d(ii) can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups.

Construction of some hypergroups from combinatorial structures.

Jajcay's studies (1993; 1994) on the automorphism groups of Cayley maps yielded a new product of groups, which he called, rotary product. Using this product, we define a hyperoperation [symbol: see text] on the group Syme(G), the stabilizer of the identity e [symbol: see text] G in the group Sym(G). We prove that (Syme(G), [symbol: see text]) is a hypergroup and characterize the subhypergroups of this hypergroup. Finally, we show that the set of all subhypergroups of Syme(G) constitute a lattice under ordinary join and meet and that the minimal elements of order two of this lattice is a subgroup of Aut(G).