Maximal resonant sets of benzenoid sistems and hypercubs of their resonance graphs

Glavno področje diplomskega dela je poiskati povezavo med maksimalnimi resonantnimi množicami benzenoidnega sistema in podgrafi resonančnega grafa, ki so maksimalne hiperkocke. Tema diplomskega dela se navezuje na področje kemijske teorije grafov, zato so v prvem delu predstavljeni osnovni pojmi in definicije kemijske teorije grafov. V drugem delu so obravnavani osnovni pojmi benzenoidnih sistemov in njihovih grafov, Kekuléjeve strukture in Clarove formule benzenoidnega sistema ter prikaz Clarovih formul z resonantnimi množicami. Resonančni grafi benzenoidnih sistemov so predstavljeni v tretjem delu. Zadnje poglavje je posvečeno obravnavi podgrafov resonančnega grafa benzenoidnega sistema ter povezavi med maksimalnimi resonantnimi množicami benzenoidnega sistema in podgrafi resonančnega grafa, ki so maksimalne hiperkocke. Glavni rezultat kaže na to, da je število Clarovih formul benzenoidnega sistema G enako številu podgrafov resonančnega grafa R(G), izomorfnih Cl(G)-dimenzionalnim hiperkockam, kjer oznaka Cl(G) označuje Clarovo število benzenoidnega sistema G.The main topic of this diploma thesis is to find the connection between maximal resonant sets of a benzenoid system and subgraphs of its resonance graph, which are maximal hypercubes. The theme of the diploma belongs to the area of chemical graph theory, therefore, certain basic facts and definitions of chemical graph theory are presented in the first part. In the second part, we deal with certain basic facts of benzenoid systems and their graphs, Kekulé structures and Clar formulas of benzenoid system and the presentation of Clar formulas with resonant sets. Resonant graphs of benzenoid systems are presented in the third part. The last chapter is devoted to subgraphs of a resonance graph of a benzenoid system and their connection to maximal resonant sets of the benzenoid system. The main result indicates that the number of Clar formulas of benzenoid system G is equal to the number of subgraphs of resonant graph R(G) isomorphic to the Cl(G)-dimenzional hypercubes, where Cl(G) denotes the Clar number of benzenoid system G