(SI) Fulereni in benzenoidi so pomembne kemijske spojine. V matematični kemiji jih modeliramo s fulerenskimi grafi in benzenoidnimi grafi. Veliko obstoječe literature na področju matematične kemije se posveča njihovim matematičnim lastnostim. Raziskovanje bo potekalo v več smereh hkrati. Znano je, da so fulereni kritično odvisni od razporeditve njihovih 12 petkotniških lic, ki so vselej prisotna. Obstaja neskončno mnogo tako imenovanih IPR-fulerenov (pravilo izoliranih petkotnikov, angl. Isolated Pentagon Rule). Preučili bomo tudi povezavo med konveksnostnim primanjkljajem ter Clarovimi in Friesovimi števili benzenoidov. Obe skupini sta v preteklosti preučevali iste družine kemijskih grafov iz različnih vidikov. Verjamemo, da lahko z združevanjem naših metod in znanj pridemo do novih zanimivih rezultatov.

(EN) Fullerenes and benzenoids are important chemical compounds. In mathematical chemistry, they are modeled by fullerene graphs and benzenoid graphs. Much of the existing literature in mathematical chemistry focuses on their mathematical properties. The research will be carried out in several directions simultaneously. It is known that fullerenes critically depend on the arrangement of their 12 pentagonal faces, which are always present. There are infinitely many so-called IPR-fullerenes (Isolated Pentagon Rule). We will also examine the relationship between convexity deficiency and the Clare and Fries numbers of benzenoids. Both groups have in the past studied the same families of chemical graphs from different perspectives. We believe that by combining our methods and knowledge, we can come up with new interesting results.