Computational aspects of two important biochemical networks with respect to some novel molecular descriptors

Quantitative structure-activity relationship (QSAR) represents quantitative correlation of biological structural features (called as topological indices) and pharmacological activity as response endpoints. Topological index is a molecular descriptor extensively used to study QSAR of pharmaceutical to assess their molecular characteristics by numerical computation. Meanwhile, the topological indices are numerical functions which are used to predict the growth rate of microorganisms in biological networks. Theoretical assessment of microorganism, such as bacteria and viruses help to expedite the vaccine design and discovery process by rationalizing the lead identification, lead optimization and understanding their mechanism of actions. Hypertree, a network structure derived from graph theory, has a great importance in biological networks for growth of microorganisms, such as bacteria and viruses. In this article, some novel eccentric and degree based topological features of two important biological networks (hypertree and its corona product) are obtained on h-level and derived closed formulas for them. Based on the obtained topological features, the biological properties of these networks are investigated.Communicated by Ramaswamy H. Sarma.

Bounds for the general sum-connectivity index of composite graphs

The general sum-connectivity index is a molecular descriptor defined as [Formula: see text], where [Formula: see text] denotes the degree of a vertex [Formula: see text], and α is a real number. Let X be a graph; then let [Formula: see text] be the graph obtained from X by adding a new vertex [Formula: see text] corresponding to each edge of X and joining [Formula: see text] to the end vertices of the corresponding edge [Formula: see text]. In this paper we obtain the lower and upper bounds for the general sum-connectivity index of four types of graph operations involving R-graph. Additionally, we determine the bounds for the general sum-connectivity index of line graph [Formula: see text] and rooted product of graphs.