20.500.12556/DKUM-69198 Szeged indeks povezav, pi indeks in wienerjev indeks povezav benzenoidnih sistemov Edge-Szeged index, pi indeks and edge-wiener indeks of benzenoid systems Magistrska naloga 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 naloge 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. 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. benzenoidni sistem topološki indeks Wienerjev indeks povezav Szeged indeks povezav PI indeks uteženi graf elementarni razrez kvocientno drevo linearna časovna zahtevnost benzenoid system topological index edge Wiener index edge Szeged index PI index weighted graph elementary cut quotient tree linear time true true false [D. Štunf] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2017-12-06 21:28:50 2018-01-09 14:24:01 2022-08-01 17:01:03 2019-07-11 17:24:20 2017 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17:54(043.2) 23571976 URN:SI:UM:DK:VHDRIASO MAG_Stunf_Doroteja_2017.pdf MAG_Stunf_Doroteja_2017.pdf 1 35AEE769A55B950FD424478E8F6E048B 4494e8287a2fa20205043858a857710914a4b083156a7dd83338a0cf06b66ff6 8d70f8fd-7c0f-11eb-bb7a-00155d0001ca 20.500.12556/dkum/ee0def4c-d7ed-4261-b2ec-8875e4fe1e85 https://dk.um.si/Dokument.php?lang=slv&id=120845 Fakulteta za naravoslovje in matematiko 0 0 0