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Title:Alianse v grafih
Authors:ID Zupanc, Tina (Author)
ID Jakovac, Marko (Mentor) More about this mentor... New window
Files:.pdf MAG_Zupanc_Tina_2016.pdf (1,14 MB)
MD5: 69B55174034992825F23DE214065278E
 
Language:Slovenian
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V magistrskem delu so predstavljene alianse v grafih, s temeljitejšo študijo pa se osredotočimo na obrambne in napadalne alianse. Definicije proučevanih pojmov so podprte s primeri in razlago, predvsem pa se v posameznih podpoglavjih posvečamo lastnostim alians. V nekaterih družinah grafov podamo natančne vrednosti obrambnih in napadalnih števil, ki sta definirani kot moč najmanjše alianse v grafu, v splošnih grafih pa moči alians navzdol in navzgor omejimo. Poglavji o obrambnih in napadalnih aliansah razširimo z definicijami globalnih alians, k-alians in globalnih k-alians ter podamo vrednosti, ki določajo natančno moč omenjenih množic ali predstavljajo spodnjo ter zgornjo mejo. V zadnjem delu magistrske naloge so omenjene močne alianse, za katere velja, da so hkrati obrambne in napadalne alianse. Zadnji razmislek je posvečen varnim množicam, ki so boljša aproksimacija realnih situacij v primerjavi z obrambnimi aliansami.
Keywords:aliansa, obrambna aliansa, napadalna aliansa, globalna obrambna aliansa, globalna napadalna aliansa, k-aliansa, dominantna množica
Place of publishing:Maribor
Publisher:[T. Zupanc]
Year of publishing:2016
PID:20.500.12556/DKUM-58726 New window
UDC:519.171(043.2)
COBISS.SI-ID:22336264 New window
NUK URN:URN:SI:UM:DK:LBFID8FN
Publication date in DKUM:19.07.2016
Views:1306
Downloads:169
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:Alliances in graphs
Abstract:In this master's thesis alliances in graphs are presented with a more thorough study focuses on defensive and offensive alliances. Definitions of concepts are supported with examples and explanations. In subsections are mostly explored properties of alliances. In some families of graphs the exact values of the defensive and offensive numbers are given, which are defined as the minimum cardinality of an alliance in the graph, whereas in general graphs the lower and upper bounds of the alliance number are set. Chapters of the defensive and offensive alliances are expanded with definitions of global alliances, k-alliances and global k-alliances and the exact values or a lower and upper bound of the minimum cardinality of these alliances are given. In the last part of the thesis strong alliances are mentioned, which are both defensive and offensive alliances. The last consideration is devoted to secure sets, which are better approximation of real situations in comparison with defensive alliances.
Keywords:alliance, defensive alliance, offensive alliance, global defensive alliance, global offensive alliance, k-alliance, dominating set


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