Barbara Ikica: On several extremal problems in chemical graph theory

Povzetek. Topological indices of molecular graphs are widely used in chemical graph theory and related disciplines in order to establish correlations between the structure of a chemical compound and its physicochemical, pharmacological, and toxicological properties.

In this talk, we focus on three such indices – on the well-established Wiener index, on the degree-based atom-bond connectivity (ABC) index, and on a distance-based analogue of the latter – more precisely, on the Graovac-Ghorbani (GG) index. We provide an overview of some recent results on problems concerning the characterisation of graphs for which the extremal values of these indices are attained. Along the way, we also discuss some related open questions as a potential extension of this work.