Degree-based Descriptors Research Articles

Computation of Structural Descriptors of Pyrene Cored Dendrimers through Quotient Graph Approach and Its Graph Entropy Measures

Dendrimers are highly defined hyperbranched artificial macromolecules, synthesised by convergent or divergent approach with specific applications in various fields. Dendrimers can be represented as graph models, from which a quantitative description can be drawn in relation with their structural properties. The distance-based and the degree-based descriptors have great importance and huge applications in structural chemistry. These indices together with entropy measures are found to be more effective and have found application in scientific fields. The idea of graph entropy is to characterise the complexity of graphs. The use of these graph invariants in quantitative structure property relationship and quantitative structure activity relationship studies has become of major interest in recent years. In this paper, the distance-based molecular descriptors of pyrene cored dendrimers are studied applying the technique of converting original graph into quotient graphs using Θ∗-classes. It is to be noted that, since the pyrene cored dendrimer, Gn is not a partial cube, usual cut method is not applicable. Further, various degree-based descriptors and their corresponding graph entropies of the pyrene cored dendrimers are also studied. Based on the obtained results, a comparative analysis as well as a regression analysis was carried out.

Novel molecular hybrid geometric-harmonic-Zagreb degree based descriptors and their efficacy in QSPR studies of polycyclic aromatic hydrocarbons

ABSTRACT The physicochemical characteristics of polycyclic aromatic compounds critical to environmental modelling such as octanol partition coefficients, solubility, lipophilicity, polarity and several equilibrium constants are functions of their underlying molecular structures, prompting the development of mathematical models to predict such characteristics for which experimental results are difficult to obtain. We propose twelve novel descriptors derived from geometric, harmonic and Zagreb degree-based descriptors and then test the effectiveness of these descriptors on a data set consisting of 55 benzenoid hydrocarbons of environmental importance. Our computations show that the proposed descriptors have a good linear correlation and predictive power when compared to the degree and distance type descriptors. We have also derived the QSPR expressions for four properties of a large series of polycyclic aromatics arising from circumscribing coronenes and show that a scaling factor can be deduced to derive physicochemical properties of such series up to 2D graphene sheets.

On Analysis and Computation of Degree-Based Topological Invariants for Cyclic Mesh Network

Recently, there has been increasing attention on the system network due to its promising applications in parallel hanging architectures such as distributed computing (Day (2004), Day and Al-Ayyoub (2002)). Related networks differ in the circumstances of topology, and the descriptors were freshly examined by Hayat and Imran (2014) and Hayat et al. (2014). Distance-based descriptors, counting-related descriptors, and degree-based descriptors are all examples of topological descriptors. These topological characteristics are linked to chemical features of a substance, such as stability, strain energy, and boiling point. The specifications for the 1st Zagreb alpha, 1st Zagreb beta, 2nd Zagreb, sum-connectivity, geometric-arithmetic, Randic, harmonic, and atom-bond connectivity indices for mesh networks M N m × n based on VE and EV degree are discussed in this paper.

Computational Analysis of new Degree-based descriptors of oxide networks

AbstractOxide networks have diverse applications in the polymer and pharmaceutical industries. Polynomials and degree-based topological indices have tendencies to correlate properties of molecular graphs. In this article, we formulate the closed forms of Zagreb and forgotten polynomials and topological indices such as Hyper-Zagreb index, first and second multiple Zagreb indices, forgotten index, Albert index, Bell index, IRM(G) of oxide networks. We also compute the F-index of complement of oxide networks, F-coindex of G and F-coindex of complement of oxide networks. We put graphical analysis of each index with respect to the parameter involved in each case.