Iranian Journal of Mathematical Chemistry
Year:2012 | Volume:3 | Issue:2|Papers Count:12

A recently published paper [T. Doslic, this journal 3 (2012) 25-34] considers the Zagreb indices of benzenoid systems, and points out their low discriminativity. We show that analogous results hold for a variety of vertex-degree-based molecular structure descriptors that are being studied in contemporary mathematical chemistry. We also show that these results are straightforwardly obtained by using some identities, well known in the theory of benzenoid hydrocarbons.

Electrode potential of 2-(2,3-dihydroxy phenyl)-1,3-dithiane (DPD) was investigated by means of cyclic voltammetry (CV) at various potential scan rates. The calculated value was compared with the experimental value obtained by cyclic voltammetry (CV). All experiments were done in aqueous phosphate buffer solutions at different pHs. The experimental redox potential of DPD was obtained to be 0.753 V versus SHE (Standard Hydrogen Electrode). DFT-B3LYP calculations using 6-311++G** basis set were performed to calculate the absolute redox potential of DPD. The calculated value of the redox potential relative to SHE is 0.766 V which is in good agreement with the experimental value (0.753).

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this  aper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

The unitary Cayley graph Xn has vertex set Zn={0, 1,…, n-1} and vertices u and v are adjacent, if gcd(u-v, n)=1. In [A. Ilic, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paperthe Wiener and hyper-Wiener index of Xn is computed.

Let G be a simple graph and  c(G,l) denotes the number of proper vertex colourings of G with at most l colours, which is for a fixed graph G, a polynomial in l , which is called the chromatic polynomial of G. Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.

The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.

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A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate this method to all classes of regular tessellations. In addition, we obtain the vertex Szeged and vertex PI indices of regular tessellations.

In this paper, we consider RNA structures with arc-length³ 4 . First, we represent these structures as matrix models and zero-one linearprogramming problems. Then, we obtain an optimal solution for this problemusing an implicit enumeration method. The optimal solution corresponds toan RNA structure with the maximum number of hydrogen bonds.

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space  fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme wediscretize the space derivative with a fourth-order compact scheme and use the Grunwald-Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme and analyze the solvability, stability and convergence of proposed scheme using the Fourier method. The convergence order of method is O (t+h4). Numerical examples demonstrate the theoretical results and high accuracy of proposed scheme.