Some Degree-Based Topological Indices of Hexagonal Cacti

Abstract

Applications of graph theory in the theoretical investigation of molecular physiochemical properties are the focus of mathematical chemistry. Atoms without hydrogen are the nodes of a chemical network, and covalent bonds between them serve as the edges. Cactus graphs are specially connected graphs in which no edge is part of more than one cycle. A topological index is a number calculated from the graph. In this work, we develop precise formulas for the randic index, geometric arithmetic index, and the atom bond connectivity index and second zagreb index, $ABC_{4}$ index and $GA_{5}$ index of hexagonal cacti, many of which are not a hexagonal chain.