20.500.12556/DKUM-57242 Maksimalne resonantne množice benzenoidnih sistemov in hiperkocke njihovih resonančnih grafov 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. benzenoidni sistem Kekuléjeva struktura popolno prirejanje Clarova formula Clarovo število resonantna množica maksimalna resonantna množica resonančni graf hiperkocka benzenoid system Kekulé structure perfect matching Clar formula Clar number resonant set maximal resonant set resonance graph hypercube true true false [B. Robič] Slovenski jezik Angleški jezik Diplomsko delo 2016-02-03 09:05:15 2016-03-03 14:27:45 2022-06-13 03:06:46 2021-05-16 03:14:57 2016 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.156(043.2) 21997576 URN:SI:UM:DK:DDLQIIAQ UN_Robic_Bojana_2016.pdf UN_Robic_Bojana_2016.pdf 1 3D97681C5B80552368930D1DDBE19862 7ce7011f38dc6b9086074ab15d18206a363a5926b481e1cacd0381e6e6e6b28a e4cd3000-7c0b-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=85954 Fakulteta za naravoslovje in matematiko 0 0 0