Wagner, StephanGutman, Ivan2021-04-202021-04-2020100167-8019https://scidar.kg.ac.rs/handle/123456789/10121The Hosoya index and the Merrifield-Simmons index are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure. In recent years, quite a lot of work has been done on the extremal problem for these two indices, i.e., the problem of determining the graphs within certain prescribed classes that maximize or minimize the index value. This survey collects and classifies these results, and also provides some useful auxiliary results, tools and techniques that are frequently used in the study of this type of problem. © 2010 Springer Science+Business Media B.V.restrictedAccessarticle10.1007/s10440-010-9575-52-s2.0-78651387791