Clarove formule benzenoidnega sistema in resonančni graf

diplomsko delo

Nina Pomberg (Author), Petra Žigert Pleteršek (Mentor)

Abstract

V diplomskem delu z naslovom Clarove formule benzenoidnega sistema in resonančni graf je obravnavana tematika iz področja kemijske teorije grafov. Diplomsko delo obravnava povezavo med Clarovimi formulami Kekulejevega benzenoidnega sistema in maksimalnimi hiperkockami pripadajočega resonančnega grafa. Na začetku so predstavljeni osnovni pojmi in definicije teorije grafov. V nadaljevanju so obravnavani benzenoidni ogljikovodiki in njihova grafična reprezentacija v obliki benzenoidnih sistemov. Obravnavane so Kekuléjeve strukture in Clarove formule benzenoidnega sistema ter predstavitev Clarovih formul z resonantnimi množicami. V osrednjem delu so obravnavani resonančni grafi benzenoidnega sistema, njihovi pod grafi, ki so izomorfni k-dimenzionalnim hiperkockam, ter povezava med Clarovimi formulami Kekuléjevega benzenoidnega sistema in maksimalnimi hiperkockami pripadajočega resonančnega grafa. Končna ugotovitev kaže na to, da je število Clarovih formul Kekuléjevega benzenoidnega sistema B enako številu podgrafov pripadajočega resonančnega grafa R(B), ki so izomorfni Cl(B)-dimenzionalni hiperkocki, kjer Cl(B) označuje Clarovo število danega benzenoidnega sistema.

Keywords

diplomska dela;matematika;benzenoidni sistem;Clarova formula;Clarovo število;resonantna množica;resonančni graf;

Data

Language:	Slovenian
Year of publishing:	2012
Source:	Žice
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Pomberg]
UDC:	51(043.2)
COBISS:	19322376
Views:	1838
Downloads:	89
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	THE CLAR FORMULAS OF A BENZENOID SYSTEM AND THE RESONANCE GRAPH
Secondary abstract:	This diploma work titled The Clar formulas of benzenoid system and the resonance graph is the subject of area of a chemical graph theory. Diploma work deals with the connection between Clar formulas of a Kekuléan benzenoid system and maximal hypercubes of the corresponding resonance graph. Basic concepts and definitions of graph theory are presented at the beginning. The following section discusses benzenoid hydrocarbons and its graphical representation in the form of benzenoid systems. Kekulé structures, Clar formulas of benzenoid systems and the presentation of Clar formulas with resonant sets are also discussed. In the main part the resonance graph of a benzenoid system, its subgraphs which are isomorphic to a k-dimensional hypercube and the connection between Clar formulas of a Kekuléan benzenoid system and the maximal hypercubes of a corresponding resonance graph are presented. The final conclusion indicates that the number of Clar formulas of a Kekuléan benzenoid system B is equal to the number of subgraphs of the resonance graph of B isomorphic to the Cl(B)-dimensional hypercube, where Cl(B) is the Clar number of B.
Secondary keywords:	benzenoid system;Kekulé structure;1-factor;Clar formula;Clar number;resonant set;resonance graph;hypercube;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	45 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	1026280