Bounds, formulas, and usefulness of graph vulnerability measures and topological indices

Determine bounds, formulas, and practical usefulness for graph vulnerability measures and topological indices, including those used to assess communication-network stability and model chemical compounds.

Background

The paper studies Hosoya polynomials of Mycielskian graphs and uses them to derive formulas for several graph vulnerability measures and topological indices, including closeness, betweenness centrality, the Wiener index, the Hyper-Wiener index, the TSZ index, and the Harary index. The conclusion places these results within the broader research direction of determining bounds, formulas, and applications for the many vulnerability measures and topological indices used in network science and mathematical chemistry.