Arithmetic-Geometric Index in Various Signed Graphs

Abstract

A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analysed the degree-based topological indices such as positive arithmetic- geometric index (  index) and negative arithmetic- geometric index (  index). Further investigated the  index) and  index in regular graph, complete graph, complete bipartite graph, union of graphs and join of graphs are derived. Further explain the theorem by examples.