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Neodvisnostno število grafa
ID Šere, Nina (Author), ID Šparl, Primož (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/6371/ This link opens in a new window

Abstract
V magistrskem delu se ukvarjamo s problemom določanja neodvisnostnega števila grafa. S pomočjo prevedbe problema 3-SAT na pripadajoči odločitveni problem o obstoju neodvisnostne množice dane velikosti najprej pokažemo, da ga uvrščamo med tako imenovane NP-polne probleme. Nato se osredotočimo na določanje neodvisnostnega števila za različne grafe. Določimo ga za nekatere dobro znane družine grafov, kot so polni grafi, polni večdelni grafi, cikli, hiperkocke itd. Posvetimo se tudi znani družini posplošenih Petersenovih grafov GP(n,k). Glede na konstrukcijo te družine je jasno, da je zgornja meja neodvisnostnega števila za GP(n,k) največ n, če pa je n liho število, pa celo največ n-1. V magistrskem delu raziskujemo, kakšna je prava vrednost neodvisnostnega števila za različne vrednosti parametra k in s tem ugotavljamo, kako dobra (oziroma slaba) je omenjena zgornja meja.

Language:Slovenian
Keywords:neodvisnostna množica
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:PEF - Faculty of Education
Year:2020
PID:20.500.12556/RUL-119326 This link opens in a new window
COBISS.SI-ID:27336195 This link opens in a new window
Publication date in RUL:14.09.2020
Views:1160
Downloads:159
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Secondary language

Language:English
Title:The independence number of a graph
Abstract:
In the master's thesis we are dealing with the independence number of a graph. We show, that the well-known problem 3-SAT is reducible to the corresponding decision problem, the so-called independent set problem, which proves that the independent set problem is NP-complete. We then determine the independence number for different graphs, including some very well known infinite families of graphs like complete graphs, multi-partite complete graphs, cycle graphs, hypercube graphs, etc. In the last part of the thesis we focus on the family of generalized Petersen graphs GP(n,k). Based on their construction it is clear, that n is the upper bound for the independence number for GP(n,k). Moreover, if n is odd, the upper bound is n-1. In the master's thesis we determine the exact value of the independence number for different values of parameter k.

Keywords:independent set

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