Showing papers in "Iranian journal of mathematical chemistry in 2015"
TL;DR: In this article, it was shown that degree-based topological indices can be easily computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the $M$-polynomial.
Abstract: Let $G$ be a graph and let $m_{ij}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The {em $M$-polynomial} of $G$ is introduced with $displaystyle{M(G;x,y) = sum_{ile j} m_{ij}(G)x^iy^j}$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the $M$-polynomial. The new approach is also illustrated with examples.
95 citations
TL;DR: In this paper, the harmonic index H(G) of a graph G is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in E(G), where deg (u) denotes the degree of a vertex u in V(G).
Abstract: The harmonic index H(G) , of a graph G is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in E(G), where deg (u) denotes the degree of a vertex u in V(G). In this paper we define the harmonic polynomial of G. We present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in Caterpillars withf diameter 4.
16 citations
TL;DR: In this paper, the authors introduced fractional-order into a model of HIV-1 infection of CD4+ T-cells and studied the effect of changing the average number of viral particles with different sets of initial conditions on the dynamics of the presented model.
Abstract: In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4^+ T--cells. We study the effect of the changing the average number of viral particles $N$ with different sets of initial conditions on the dynamics of the presented model. The nonstandard finite difference (NSFD) scheme is implemented to study the dynamic behaviors in the fractional--order HIV-1 infection model. Numerical results show that the NSFD approach is easy to be implemented and accurated when applied to fractional-order HIV-1 infection model.
15 citations
TL;DR: In this paper, a two-step trigonometrically fitted symmetric Obrechkoff method was proposed for solving IVPs with periodic solutions such as orbital problems, and the numerical results obtained by the new method for some problems show its superiority in efficiency, accuracy and stability.
Abstract: In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numerical results obtained by the new method for some problems show its superiority in efficiency, accuracy and stability.
13 citations
TL;DR: In this paper, the authors discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos.
Abstract: In this paper, we discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. We study the synchronization of chemical reactors model via sliding mode control scheme. The stability of this proposed method is proved by Barbalate's lemma. Numerical Simulation is provided for illustration and verification of the proposed method.
9 citations
TL;DR: The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper-Wiener indices, degree distance, and many others), are expressed in terms of contributions.
Abstract: The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges.
8 citations
TL;DR: In this article, the relationship between the Randic', Balaban and Szeged indices and Harary numbers to the enthalpies of combustion (C H sub H ) of monocarboxylic acids (C2C20) are established.
Abstract: Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indices for examination of structure- property relationship is Randic' index. In this study is represented the relationship between the Randic', Balaban and Szeged indices and Harary numbers to the enthalpies of combustion ( C H sub H ) of monocarboxylic acids (C2C20) are established, and then, some useful topological indices for examination of the structure- property relationship are presented.
5 citations
TL;DR: The energy of a graph is equal to the sum of the absolute values of its eigenvalues, and two graphs of the same order are said to be equienergetic if their energies are equal as mentioned in this paper.
Abstract: The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pair. (2) If by numerical calculation one finds that two non- cospectral graphs seem to be equienergetic, in the general case no method is known for proving that this indeed is the case.
3 citations
TL;DR: In this paper, a rapid and sensitive method was used for the direct determination of gallic acid and caffeine in green tea that is based on excitation-emission data using chemometric approaches.
Abstract: Green tea is considered as a dietary source of antioxidant nutrients, which acts upon human health. Green tea leaves contain three main components in the form of simple hydroxy benzoic acids such as gallic acid, propyl gallate and xanthic bases (caffeine), have been reported to prevent or delay a number of degenerative diseases and act mainly upon the central nervous system and stimulating wakefulness. Therefore, it is important to establish a simple and reliable analytical method for determination of these compounds in the presence of unexpected interferences in the green tea sample. In this research, a rapid and sensitive method was used for the direct determination of gallic acid and caffeine in green tea that is based on excitation-emission data using chemometric approaches. Multi-way chemometric models can be used to study such data, providing estimates of the spectra and concentration profiles of the underlying chemical analytes. A high percentage of recoveries for the spiked green tea for gallic acid (i.e. 96.15 %-109.78 %) and caffeine (i.e. 93.75% -101.57%) indicate the high accuracies of the proposed calibration methods for the assessment of gallic acid and caffeine in green tea
3 citations
TL;DR: In this paper, the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices, was obtained by using the Gini index, where d denotes the degree of a vertex u∈V(G).
Abstract: The total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈V(G). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.
3 citations
TL;DR: In this article, the acyclic chromatic index of a graph G is defined as the minimum number of colors k such that there is a proper edge coloring using k colors.
Abstract: An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph G denoted by ) ( ' G a is the minimum number k such that there is an acyclic edge coloring using k colors. The maximum degree in G denoted by ∆(G), is the lower bound for ) ( ' G a . Pcuts introduced in this paper
TL;DR: In this paper, the reliability Wiener number of a Cartesian product of graphs is derived and the model considered here is taken into account and at the same time the conceptual simplicity of the discrete graph theoretical model is preserved.
Abstract: Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain conditions the bonds can break with certain probability. This is fully taken into account in quantum chemistry. In the model considered here, probabilistic nature is taken into account and at the same time the conceptual simplicity of the discrete graph theoretical model is preserved. Here we extend previous studies by deriving a formula for the reliability Wiener number of a Cartesian product of graphs.
TL;DR: In this paper, the Co-PI matrix of G is shown to have some inequalities involving the topological indices, the number of vertices and edges, and the maximum degree.
Abstract: In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.
TL;DR: In this article, it was shown that the matching interdiction problem in the weighted graph G is for dendrimers, and that the ratio in these classes of dendrrimers is equal to the maximum value.
Abstract: The purpose of the matching interdiction problem in the weighted graph G is for them. It is shown that this ratio in these classes of dendrimers is equal to the maximum value.
TL;DR: In this article, a distance-based topological index of Hphenylenic nanotorus was proposed. But it is not an exact formula for the Wiener index.
Abstract: Let G be a connected simple (molecular) graph. The distance d(i, j) between two vertices i and j of G is equal to the length of a shortest path that connects i and j. In this paper we compute some distance based topological indices of Hphenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As an application the Schultz index and modified Schultz index of this graph will be computed by using whose Wiener index. Finally, we compute eccentric connectivity index of this graph.
TL;DR: Hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established in this paper, where the authors considered the problem of constructing a hyper-cube of n dimensions.
Abstract: Hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established.