ON CERTAIN TOPOLOGICAL INDICES OF BENZENOID COMPOUNDS

Drug discovery is mainly the result of chance discovery and massive screening of large corporate libraries of synthesized or naturally-occurring compounds. Computer aided drug design is an approach to rational drug design made possible by the recent advances in computational chemistry in various fields of chemistry, such as molecular graphics, molecular mechanics, quantum chemistry, molecular dynamics, library searching, prediction of physical, chemical, and biological properties.  The structure of a chemical compound can be represented by a graph whose vertex and edge specify the atom and bonds respectively. Topological indices are designed basically by transforming a molecular graph into a number. A topological index is a numeric quantity of a molecule that is mathematically derived from the structural graph of a molecule. In this paper we compute certain topological indices of pyrene molecular graph. The topological indices are used in quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) studies.Â

Sharp bounds for the general Randić index of graphs with fixed number of vertices and cyclomatic number

The cyclomatic number, denoted by $\gamma$, of a graph $G$ is the minimum number of edges of $G$ whose removal makes $G$ acyclic. Let $\mathscr{G}_{n}^{\gamma}$ be the class of all connected graphs with order $n$ and cyclomatic number $\gamma$. In this paper, we characterized the graphs in $\mathscr{G}_{n}^{\gamma}$ with minimum general Randić index for $\gamma\geq 3$ and $1\leq\alpha\leq \frac{39}{25}$. These extend the main result proved by A. Ali, K. C. Das and S. Akhter in 2022. The elements of $\mathscr{G}_{n}^{\gamma}$ with maximum general Randić index were also completely determined for $\gamma\geq 3$ and $\alpha\geq 1$

Symmetry in Graph Theory

This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view