Dominacijske množice na grafih : delo diplomskega seminarja

Sovdat, Veronika (author), Potočnik, Primož (mentor), Vidali, Janoš (comentor)

V diplomski nalogi obravnavam dominacijske množice na grafih. Raziskala sem različne algoritme za iskanje najmanjše dominacijske množice in njenih približkov. Algoritme sem preizkusila na različnih modelih grafov. Raziskala sem natančnost približnih metod za različne modele grafov in časovne zahtevnosti algoritmov za vsak model grafov posebej. S simulacijami sem potrdila oceno za natančnost požrešne metode, ki sem jo predhodno teoretično dokazala. Ocena je zelo dobra za model Erdős–Rényijevih grafov. Velja tudi za Barabási–Albertov model, čeprev bi se za slednji model dalo dobiti tudi nižjo zgornjo mejo.

• Language: Slovenian
• Keywords: Dominacijska množica, najmanjša dominacijska množica, modeli grafov
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-120203
• UDC: 519.17
• COBISS.SI-ID: 54858243
• Publication date in RUL: 17.09.2020

Secondary language

• Language: English
• Title: Dominating sets in graphs

Abstract

In my dissertation, I focus on the dominating set in graphs. I have researched different algorithms to find the minimum dominating sets and their approximations. I have tested the algorithms on different graph models. I have investigated the accuracy of various methods on various models of graphs and their time complexities. With the simulations, I have confirmed the estimate for the accuracy of the greedy method, which I had previously proved theoretically. The estimate is very good for the Erdős--Rényi graph model. It also applies to the Barabási--Albert model, although a lower upper bound could be obtained for this kind of graphs.

• Keywords: Dominating set, minimum dominating set, graph models