Eccentricity-Based Topological Indices of Chain Graphs

This article delves into the realm of eccentricity-based topological indices, focusing particularly on a class of graphs called chain graphs. Topological indices serve as numerical descriptors derived from molecular structures, aiding in the elucidation of chemical properties and activities. Today, topological indices remain a vibrant area of research, with applications spanning various fields of chemistry, including drug design, materials science, environmental chemistry, and bioinformatics. Chain graphs are a special class of bipartite graphs having the largest spectral radius among all the bipartite graphs of prescribed order and size. Nevertheless, the high significance of chain graphs in the field of spectral graph theory, the domain of various topological indices remains unexplored. This article categorizes generalized eccentricity-based topological indices into two types and explores them. Some of the major eccentricity-based topological indices like the total eccentricity index, Zagreb eccentricity indices, ABC eccentricity index, and geometric-arithmetic eccentricity index of chain graphs are studied in detail and an inequality connecting their relationship is provided. Further, the extremities for these indices among chain graphs are presented.