Iranian Journal of Mathematical Chemistry
Volume:2 Issue: 1, Spring-Summer 2011

Hyperdiamonds are covalently bonded fullerenes in crystalline forms, more or less related to diamond, and having a significant amount of sp3 carbon atoms. Design of severalhypothetical crystal networks was performed by using our original software programsCVNET and NANO-STUDIO. The topology of the networks is described in terms of the netparameters and several counting polynomials, calculated by NANO-STUDIO, OMEGA andPI software programs.

In the present work we study the use of Fourier transform near infrared spectroscopy (FTNIRS) technique to analysis the calcium (Ca), phosphorus (P) and copper (Cu) contents of fish meal. The regression methods employed were partial least squares (PLS) and kernel partial least squares (KPLS). The results showed that the efficiency of KPLS was better than PLS. As a whole, the application of FT-NIRS with PLS and KPLS was as a suitable option for replacing the routine chemical analysis to assess the mineral content in fish meal, allowing immediate control of the fish meal without prior sample treatment or destruction.

Let R be a commutative ring and Γ(R) be its zero−divisor graph. In this article, we study Wiener index and energy of Γ(Zn) where n = pq or n =and p, q are primes. A MATLABcode for our calculations is also presented.

A fullerene graph is a 3connected planar graph whose faces are pentagons and hexagons. The Clar number of a fullerene is the maximum size of sextet patterns, the sets of disjoint hexagons which are all M-alternating for a Kekulé structure M of F. An exact formula of Clar number of some fullerene graphs and a class of carbon nanocones are obtained in this paper.

The Wiener polarity index Wp(G) of a molecular graph G of order n is the number ofunordered pairs of vertices u, v of G such that the distance d(u,v) between u and v is 3. In an earlier paper, some extremal properties of this graph invariant in the class of catacondensed hexagonal systems and fullerene graphs were investigated. In this paper, some new bounds for this graph invariant are presented. A relationship between Wiener and Wiener polarity index of some classes of graphs are also presented.

Let G be a simple graph. The Hosoya polynomial of G is (,) (,) = {,} () v xd u H G x  u v V G where d(u,v) denotes the distance between vertices u and v. The dendrimer nanostar is a part of a new group of macromolecules. In this paper we compute the Hosoya polynomial for an infinite family of dendrimer nanostar. As a consequence we obtain the Wiener index and the hyper-Wiener index of this dendrimer.

Let G be a simple connected graph and {v1, v2, …, vk} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)– entry is the topological distance between vi and vj of G. In this paper, we obtain the spectrum of the reduced distance matrix of thorn graph of G, a graph which obtained by attaching some new vertices to pendent vertices of G. As an application we compute the spectrum of reduced distance matrix for some dendrimer graphs.

In this paper, a new molecular-structure descriptor, the general sum–connectivity co index is considered, which generalizes the first Zagreb co–index and the general sum– connectivity index of graph theory. We mainly explore the lower and upper bounds in terms of the order and size for this new invariant. Additionally, the Nordhaus–Gaddum–type result is also represented.

Fullerenes are closed−cage carbon molecules formed by 12 pentagonal and n/2 – 10 hexagonal faces, where n is the number of carbon atoms. Patrick Fowler in his lecture in MCC 2009 asked about the Wiener index of fullerenes in general. In this paper we respond partially to this question for an infinite class of fullerenes with exactly 10n carbon atoms. Our method is general and can be applied to fullerene graphs with centrosymmetric adjacency matrix.

A topological index of a molecular graph G is a numeric quantity related to G which is invariant under symmetry properties of G. In this paper we obtain the Randić, geometricarithmetic, first and second Zagreb indices, first and second Zagreb coindices of tensor product of two graphs and then the Harary, Schultz and modified Schultz indices of tensor product of a graph G with complete graph of order n are obtained.