magistrsko delo
Doroteja Štunf (Author), Petra Žigert Pleteršek (Mentor)

Abstract

Magistrsko delo obravnava benzenoidne sisteme. Predstavljena je uporaba teorije grafov v kemiji in s tem uporabna povezava med kemijo in matematiko. V uvodnih poglavjih so zato predstavljeni osnovni pojmi teorije grafov in kemijski pojmi, ki so potrebni za razumevanje nadaljnje snovi. Benzenoidni sistemi so zanimivi za raziskovanje, saj predstavljajo skupino kemijskih spojin imenovano benzenoidni ogljikovodiki. V nadaljevanju dela so podane osnovne lastnosti in definicije benzenoidnih sistemov. V uvodu osrednjega dela so navedene definicije Wienerjevega, Szeged in PI indeksa za poljubne in nato še za utežene grafe. Sledi vpeljava vseh treh indeksov povezav s predstavitvijo algoritmov za njihov izračun v linearni časovni zahtevnosti, ki je v nalogi tudi dokazana. Za lažje razumevanje so dodani primeri izračuna na izbranem primeru benzenoidnega sistema.

Keywords

magistrska dela;benzenoidni sistemi;topološki indeksi;Wienerjev indeks povezav;Szeged indeks povezav;PI indeks;uteženi grafi;kvocientna drevesa;linearna časovna zahtevnost;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [D. Štunf]
UDC: 519.17:54(043.2)
COBISS: 23571976 Link will open in a new window
Views: 901
Downloads: 63
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: English
Secondary title: Edge-Szeged index, pi indeks and edge-wiener indeks of benzenoid systems
Secondary abstract: The master's thesis deals with benzenoid systems. The use of the graph theory in chemistry and thus the useful connection between chemistry and mathematics is presented. Therefore, the introductory chapters outline the basic concepts of graph theory and the chemical concepts needed to understand further matter. Benzenoid systems are interesting for research because they represent a group of chemical compounds called benzenoid hydrocarbons. The basic properties and definitions of benzenoid systems are introduced in the following chapters of the thesis. The introduction of the central part of the thesis contains the definitions of Wiener's, Szeged and PI index for arbitrary and later for weighted graphs as well. Then follows the introduction of all three link indexes with the presentation of algorithms for their calculation in linear time, which is also proven in the thesis. To clarify and facilitate understanding examples of calculation for the chosen case of the benzenoid system are added at the end of the thesis.
Secondary keywords: master theses;benzenoid systems;topological indexes;edge Wiener index;edge Szeged index;PI index;weighted graphs;elementary cuts;quotient trees;linear time;
URN: URN:SI:UM:
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: 51 str.
ID: 10886920