diplomsko delo
Bojana Robič (Author), Petra Žigert Pleteršek (Mentor)

Abstract

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.

Keywords

diplomska dela;benzenoidni sistemi;Kekuléjeva struktura;popolno prirejanje;Clarova formula;Clarovo število;resonantne množice;maksimalne resonantne množice;resonančni grafi;hiperkocke;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [B. Robič]
UDC: 519.156(043.2)
COBISS: 21997576 Link will open in a new window
Views: 1008
Downloads: 80
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Other data

Secondary language: English
Secondary title: Maximal resonant sets of benzenoid sistems and hypercubs of their resonance graphs
Secondary abstract: 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.
Secondary keywords: theses;benzenoid systems;Kekulé structure;perfect matching;Clar formula;Clar number;resonant sets;maximal resonance sets;resonance graphs;hypercubes;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: 44 f.
ID: 9122965