Abdul Qudair Baig

On the metric dimension of circulant graphs

Abstract Let G = ( V , E ) be a connected graph and d ( x , y ) be the distance between the vertices x and y in V ( G ) . A subset of vertices W = { w 1 , w 2 , … , w k } is called a resolving set or locating set for G if for every two distinct vertices x , y ∈ V ( G ) , there is a vertex w i ∈ W such that d ( x , w i ) ≠ d ( y , w i ) for i = 1 , 2 , … , k . A resolving set containing the minimum number of vertices is called a metric basis for G and the number of vertices in a metric basis is its metric dimension, denoted by d i m ( G ) . Let F be a family of connected graphs G n : F = ( G n ) n ≥ 1 depending on n as follows: the order | V ( G ) | = φ ( n ) and lim n → ∞ φ ( n ) = ∞ . If there exists a constant C > 0 such that d i m ( G n ) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension. The metric dimension of a class of circulant graphs C n ( 1 , 2 ) has been determined by Javaid and Rahim (2008) [13] . In this paper, we extend this study to an infinite class of circulant graphs C n ( 1 , 2 , 3 ) . We prove that the circulant graphs C n ( 1 , 2 , 3 ) have metric dimension equal to 4 for n ≡ 2 , 3 , 4 , 5 ( mod 6 ) . For n ≡ 0 ( mod 6 ) only 5 vertices appropriately chosen suffice to resolve all the vertices of C n ( 1 , 2 , 3 ) , thus implying that d i m ( C n ( 1 , 2 , 3 ) ) ≤ 5 except n ≡ 1 ( mod 6 ) when d i m ( C n ( 1 , 2 , 3 ) ) ≤ 6 .

Margin based ontology sparse vector learning algorithm and applied in biology science

In biology field, the ontology application relates to a large amount of genetic information and chemical information of molecular structure, which makes knowledge of ontology concepts convey much information. Therefore, in mathematical notation, the dimension of vector which corresponds to the ontology concept is often very large, and thus improves the higher requirements of ontology algorithm. Under this background, we consider the designing of ontology sparse vector algorithm and application in biology. In this paper, using knowledge of marginal likelihood and marginal distribution, the optimized strategy of marginal based ontology sparse vector learning algorithm is presented. Finally, the new algorithm is applied to gene ontology and plant ontology to verify its efficiency.

On molecular topological properties of hex-derived networks

Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure–activity relationship/quantitative structure–property relationship study, physico‐chemical properties and topological indices such as Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study hex‐derived networks HDN1(n) and HDN2(n), which are generated by hexagonal network of dimension n and derive analytical closed results of general Randić index Rα(G) for different values of α, for these networks of dimension n. We also compute the general first Zagreb, ABC, GA, ABC4, and GA5 indices for these hex‐derived networks for the first time and give closed formulae of these degree‐based indices for hex‐derived networks. Copyright

Topological Characterization of the Symmetrical Structure of Bismuth Tri-Iodide

The bismuth tri-iodide ( B i I 3 ) is an inorganic compound. It is the result of the response of bismuth and iodine, which has inspired enthusiasm for subjective inorganic investigation. The topological indices are the numerical invariants of the molecular graph that portray its topology and are normally graph invariants. In 1975, Randic presented, in a bond-added substance, a topological index as a descriptor for portraying subatomic branching. In this paper, we investigate the precious stone structure of bismuth tri-iodide chain and sheet. Moreover, exact formulas of degree-based added-substance topological indices principally the first, second, and hyper Zagreb indices, the general Randic index, the geometric-arithmetic index, the fourth atom-bond connectivity index, and the fifth geometric arithmetic index of the subatomic graph of bismuth tri-iodide for both chain and sheet structures are determined.

Kinetic modeling of biomass gasification in a micro fluidized bed

ABSTRACT This paper presents a goal programming model to predict the kinetic parameters of micro fluidized bed (Micro-FB) gasification of woody biomass in Qom, Iran. Qom has an abundance of waste woody biomass, and gasification can convert this residue into clean syngas. To do this, a kinetic model of biomass gasification was developed and validated against the experimental data available in the literature. The experiments were carried out in a Micro-FB in the presence of silica sand as the fluidization medium. To fully decompose the aromatic tars, the reaction temperatures were considered between 700°C and 1000°C with 100°C intervals. Results showed that the obtained activation energies strongly depend on the particle size for all the tested conditions.

Study of biological networks using graph theory

As an effective modeling, analysis and computational tool, graph theory is widely used in biological mathematics to deal with various biology problems. In the field of microbiology, graph can express the molecular structure, where cell, gene or protein can be denoted as a vertex, and the connect element can be regarded as an edge. In this way, the biological activity characteristic can be measured via topological index computing in the corresponding graphs. In our article, we mainly study the biology features of biological networks in terms of eccentric topological indices computation. By means of graph structure analysis and distance calculating, the exact expression of several important eccentric related indices of hypertree network and X-tree are determined. The conclusions we get in this paper illustrate that the bioengineering has the promising application prospects.

Experimental study of steam-gasification of municipal solid wastes (MSW) using Ni-Cu/γ-Al 2O3 nano catalysts

ABSTRACT There is an increasing interest in the conversion of municipal solid waste (MSW) due to its low cost and high potential for production of syngas and chemicals. Gasification is a promising thermochemical process to transform carbon-based fuels into a valuable fuel/syngas. In this article, an experimental study of air-gasification of municipal solid waste (MSW) using Ni-Cu/γ-Al2O3 nano catalysts was developed. The particle sizes were ranged from 0.3 mm to 0.35 mm and loaded into the Micro-FB system at the beginning of each experiment. The influence of type of catalysts, gasification temperature and catalyst loading on tar concentration, hydrogen yield, and char conversion was evaluated. Results showed that with increasing the gasification temperature, the hydrogen yield gradually increases from 25 to 34 g/kg fuel at 600°C and 24 to 32 g/kg fuel at 800°C when using Ni/γ-Al2O3 and Cu/γ-Al2O3 catalysts, respectively. It also found that the use of metal catalyst during the gasification process is an influential parameter affecting the evolution profiles of gasification products, especially for hydrogen.

A family of fifth-order convergent methods for solving nonlinear equations using variational iteration technique

Abstract In this paper, we suggest and analyze new higher order family of iterative methods for solving nonlinear equations by using variational iteration technique. We give several examples to illustrate the efficiency of the proposed methods. Comparison with other similar methods is also given. New methods can be considered as an alternative of the existing methods. This technique can be used to suggest a wide class of new iterative methods for solving nonlinear equations.

On (a, d) -EAT labeling of subdivision of K1, r

Abstract A labeling is a mapping which gives the numbers as labels to the vertices and edges of a graph. In this paper, we investigate the class of the subdivided star г ≅ G(n, n + 1, m, m + 1, 2m + 1, n5,…, np) as a super (a, d)-EAT graphs for all possible values of d, m and n.

On Topological Indices of Fractal and Cayley Tree Type Dendrimers

The topological descriptors are the numerical invariants associated with a chemical graph and are helpful in predicting their bioactivity and physiochemical properties. These descriptors are studied and used in mathematical chemistry, medicines, and drugs designs and in other areas of applied sciences. In this paper, we study the two chemical trees, namely, the fractal tree and Cayley tree. We also compute their topological indices based on degree concept. These indices include atom bond connectivity index, geometric arithmetic index and their fourth and fifth versions, Sanskruti index, augmented Zagreb index, first and second Zagreb indices, and general Randic index for . Furthermore, we give closed analytical results of these indices for fractal trees and Cayley trees.