The Second Maximum Mostar Index of Unicyclic Graphs With Given Diameter

Topological invariants are key tools for studying the physicochemical and thermodynamic properties of chemical compounds. Recently, a new bond‐additive distance‐based graph invariant called the Mostar index has been developed. It measures the importance of individual edges and the graph as a whole. It is denoted and defined as . This invariant is helpful to characterize the structure of a given connected graph G . In this invariant, the quantity n x ( x y ) means the number of vertices closer to x than y . In the present study, first, we have considered the Mostar index of extremal unicyclic graphs of n vertices with given diameter. Second, we have determined all unicyclic graphs that contain the second maximum Mostar index.