Clarove strukture in 6-rotacijsko drevo benzenoidnega grafa

diplomsko delo

Jasna Zamuda (Author), Petra Žigert Pleteršek (Mentor)

Abstract

Glavno področje diplomskega dela je določitev grafov z enakim številom Clarovih struktur in Clarovih pokritij brez alternirajočih šestkotnikov benzenoidnih sistemov. Tema diplomskega dela se navezuje na področje teorije grafov. Zato so v prvem poglavju predstavljeni določeni osnovni pojmi teorije grafov. V nadaljevanju so obravnavani benzenoidni sistemi in grafi, Kekuléjeve strukture in 1-faktorji. Osrednje poglavje je tretje poglavje, v katerem so podane definicije in izreki o Clarovih strukturah, o 6-rotacijskem drevesu benzenoidnega grafa, o Clarovih pokritjih ter o resonančnih vzorcih. Kot osrednji rezultat je podan zadostni pogoj za enakost števila Clarovih struktur in Clarovih pokritij brez alternirajočih šestkotnikov benzenoidnega grafa.

Keywords

matematika;Clarova struktura;drevesa;benzenoidni grafi;pokritje;polinomi;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[J. Zamuda]
UDC:	51(043.2)
COBISS:	18312712
Views:	2052
Downloads:	74
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	CLAR STRUCTURES AND THE SEXTET-ROTATION TREE OF A BENZENOID GRAPH
Secondary abstract:	Main topic of this diploma paper is determination of graphs with equal number of Clar structures and Clar covers without alternating hexagons of benzenoid systems. The theme of the diploma belongs to the area of graph theory. Therefore certain basics facts of graph theory are presented in the first chapter. Following, we deal with benzenoid systems and graphs, Kekulé structures and perfect matchings. The central chapter is the third chapter, where one can find definitions and theorems about Clar structures, sextet-rotation tree benzenoid graph, Clar covers and resonant patterns. As the main result the sufficient condition for the equality between Clar structures and Clar covers without alternating hexagons of benzenoid graph is given.
Secondary keywords:	perfect matching;Clar structure;sextet-rotation tree of a benzenoid graph;Clar cover;Clar polynomial.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	39 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19214