(SI) Najprej bomo poskušali izkoristiti veliko večje poznavanje delovanja grupe avtomorfizmov na povezavah grafa, da ugotovimo, ali grupe avtomorfizmov grafov določajo grupo avtomorfizmov pripadajočih grafičnih matroidov. V kolikor se izkaže, da temu ni tako, bomo poskušali ugotoviti koliko dodatnih avtomorfizmov (simetrij) premorejo grafični matroidi glede na grafe. Nato bomo poskušali obravnavati analoge Cayleyevim grafom v splošnih matroidih in morda poiskali karakterizacijo v smislu “Sabidussi”-jeve karakterizacije za Cayleyeve grafe. Od tu se bodo naravno odpirale smeri nadaljnjega raziskovanja.

(EN) First, we will try to exploit the much greater knowledge of the action of group automorphisms on graph links to see whether the group automorphisms of graphs determine the group automorphisms of the corresponding graph matroids. If this turns out not to be the case, we will try to find out how many additional automorphisms (symmetries) the graph matroids have with respect to the graphs. We will then try to consider analogs to Cayley graphs in general matroids and perhaps find a characterization in terms of the "Sabidussi"-characterization for Cayley graphs. From here, directions for further research will naturally open up.