Dominacija in celotna dominacija v Fibonaccijevih in Lucasovih kockah : magistrsko delo

Golob, Jan (author), Klavžar, Sandi (mentor)

V delu obravnavamo problem dominantnega in celotnega dominantnega števila Fibonaccijevih in Lucasovih kock. Formula za te štiri probleme zaenkrat še ne obstajajo. V delu pa je narejena analiza trenutnih rezultatov za spodnje in zgornje meje. Spoznamo tudi izboljšavo rezultatov s pomočjo linearnega programiranja in soroden problem 2-pakirnega števila.

• Language: Slovenian
• Keywords: dominacija, celotna dominacija, Fibonaccijeve kocke, Lucasove kocke, hiperkocke
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-141652
• UDC: 519.1
• COBISS.SI-ID: 124258819
• Publication date in RUL: 04.10.2022

Secondary language

• Language: English
• Title: Domination and total domination in Fibonacci and Lucas cubes

Abstract

In the work we discuss the problem of the domination and the total domination number of Fibonacci and Lucas cubes. The exact formulas for these four problems currently do not exist. The work thus includes an analysis of lower and upper bounds. We also present the improved results obtained with the use of linear programming and a related problem of the 2-packing number.

• Keywords: domination, total domination, Fibonacci cubes, Lucas cubes, hypercubes