Topological Descriptors on Some Families of Graphs

Abstract

In view of the successful applications of graph theory, relationships between the biological activity and chemical structure have been developed. One of the popular topics in graph theory is problems relating to topological indices. Degree-based topological indices, distance-based topological indices, and counting-related topological indices are various types of topological indices. Physiochemical properties such as boiling point and stability of chemical compounds are correlated by these topological indices. A topological index of a graph is a numerical quantity obtained from the graph mathematically. A cactus graph is a connected graph in which no edge lies in more than one cycle. In this study, we have derived certain degree-based topological indices for some families of graphs consisting of graph obtained by the rooted product of paths and cycles and two types of cactus graph (paracactus and orthocactus) with the help of the generalized Zagreb index.