Shibsankar Das

Silicon carbide, often known as carborundum, is a combination of silicon and carbon. Silicon carbide is one semiconductor material that is increasingly being utilized in semiconductor devices. In 1...

In this paper, we provide the upper bound on the energy of a graph using the Diaz–Metcalf inequality. Then, we obtained several bounds on the energy of a graph with given invariants such as order, size, diameter, radius, girth, Kirchoff index, clique number, algebraic connectivity, vertex connectivity and index. Finally, we obtain several bounds on the energy of a graph in terms of many topological indices such as harmonic index, symmetric division degree index and modified second Zagreb indices.

Chemical graph theory is an important field of mathematical chemistry that deals with the mathematical modeling of chemical compound structures. A graph consisting of non-hydrogen atoms is known as a molecular graph. The reverse degree-based topological indices are an important tool in mathematical chemistry to encode the structural information of a molecular graph in the form of a fixed quantity. In this study, we are going to introduce a concept of a polynomial based on the reverse degree of a graph. Let [Formula: see text] be a graph and let [Formula: see text] be the number of [Formula: see text]-edges of [Formula: see text] such that [Formula: see text] We introduce the idea of the Reverse M-polynomial (RM-polynomial) of [Formula: see text], which is defined as [Formula: see text] This investigation presents the derivation of novel closed-form expressions for well-known reverse degree-based topological indices. Rather than employing conventional mathematical definitions, our approach utilizes the RM-polynomial framework to compute these indices for the oxide networks and the antiviral pharmaceutical agent Zanamivir. The RM-polynomial offers significant computational advantages by enabling the calculation of multiple reverse degree-based topological indices and reducing computational complexity. Furthermore, this study provides a comprehensive analysis of the graphical representations and the behavioral characteristics exhibited by the RM-polynomial and the reverse degree-based topological indices of graphs corresponding to the oxide networks and the Zanamivir graph. These results demonstrate the practical utility of the RM-polynomial approach in the field of mathematical chemistry.

In this article, we determine the extremal graphs concerning the augmented Sombor index over the connected graph (resp. chemical graph) of a given order. Then we have determined several upper and lower bounds on the augmented Sombor index of a graph with given parameters. Finally, in Sec. 3, we determine the relationships between the augmented Sombor index and other standard topological indices and also characterize the family of graphs where the bounds are reached.