On Degree-Based Topological Indices for Strong Double Graphs

A topological index is a characteristic value which represents some structural properties of a chemical graph. We study strong double graphs and their generalization to compute Zagreb indices and Zagreb coindices. We provide their explicit computing formulas along with an algorithm to generate and verify the results. We also find the relation between these indices. A 3D graphical representation and graphs are also presented to understand the dynamics of the aforementioned topological indices.

Topological properties of Sierpinski network and its application

Background: Sierpinski graphs S(n,k) are largely studied because of their fractal nature with applications in topology, chemistry, mathematics of Tower of Hanoi, and computer sciences. Applications of molecular structure descriptors are a standard procedure that are used to correlate the biological activity of molecules with their chemical structures and thus can be helpful in the field of pharmacology. Objective: The aim of this article is to establish analytically closed computing formulae for eccentricity-based descriptors of Sierpinski networks and their regularizations. These computing formulae are useful to determine a large number of properties like thermodynamic properties, physicochemical properties, chemical and biological activity of chemical graphs. Methods: At first, vertex sets have been partitioned on the basis of their degrees, eccentricities, and frequencies of occurrence. Then these partitions are used to compute the eccentricity-based indices with the aid of some combinatorics. Results: The total eccentric index and eccentric-connectivity index have been computed. We also compute some eccentricity-based Zagreb indices of the Sierpinski networks. Moreover, a comparison has also been presented in the form of graphs. Conclusion: These computations will help the readers to estimate the thermodynamic properties, physicochemical properties of chemical structures, which are of fractal nature and can not be dealt with easily. A 3D graphical representation is also presented to understand the dynamics of the aforementioned topological descriptors.

New 3D graphical representation for RNA structure analysis and its application in the pre-miRNA identification of plants

MicroRNAs (miRNAs) are a family of short non-coding RNAs that play significant roles as post-transcriptional regulators.

3D Graphical Representation of Protein Sequences Based on Conformational Parameters of Amino Acids

Based on the helix and-sheet and the-turn conformational parameters, and and , of the 20 amino acids, we propose a new 3D graphical representation of protein sequence without circuit or degeneracy, which may reflect the innate structure of the protein sequence. Then the numerical characterizations of protein graphs, the leading eigenvalues of the L/L matrices associated with the graphical curves for protein sequences, was utilized as descriptors to analyze the similarity/dissimilarity of the nine ND5 protein sequences.

Phylogenetic Analysis of H7N9 Avian Influenza Virus Based on a Novel Mathematical Descriptor

A new mathematical descriptor was proposed based on 3D graphical representation. Using the method, we construct the phylogenetic trees of nine proteins of H7N9 influenza virus to analyze the originated source of H7N9. The results show that the evolution route of H7N9 avian influenza is from America through Europe to Asia. Furthermore, two samples collected from environment in Nanjing and Zhejiang and one sample collected from chicken are the sources of H7N9 influenza virus that infected human in China.

Modeling of surfaces using 3D fractal interpolation

This paper discusses the concept of three-dimensional (3D) fractal interpolation and the possibility to use it in modeling 3D surfaces. It is important to notice that this paper treats fractal interpolation only as a numerical tool and not as a model. The purpose of the research is to create a methodology for obtaining models for the given 3D surface and making them similar to it to a certain degree. The set of models then can be investigated as required (3D graphical representation, simulation of particular technological process, quality assessment for bonded surfaces, etc.). Measuring a particular 3D surface and making a set of models is far more cost efficient than performing the measurements many times.