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Title:
Nekatere s pakiranji povezane lastnosti grafov
Authors:
ID
Božović, Dragana
(Author)
ID
Peterin, Iztok
(Mentor)
More about this mentor...
Files:
DOK_Bozovic_Dragana_2020.pdf
(753,30 KB)
MD5: 36963E8CFCD8575BFE79D14BA56455C1
PID:
20.500.12556/dkum/62090e91-73f5-4664-81e7-fbe988c419ce
Language:
Slovenian
Work type:
Doctoral dissertation
Typology:
2.08 - Doctoral Dissertation
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
V disertaciji se ukvarjamo z različnimi problemi, povezanimi s pakiranji. Disertacija je sestavljena iz štirih delov. Prvi del je namenjen grafom, ki imajo enolično pakirno množico največje moči. Najprej predstavimo nekatere lastnosti teh grafov. Nato podamo še dve karakterizaciji dreves z enolično pakirno množico. V drugem delu vpeljemo pojem dimenzije incidenčnosti, ki je neposredno povezana z 2-pakirnim številom grafa, in določimo formulo za njen izračun. Dokažemo, da je problem iskanja incidenčne dimenzije grafa v splošnem NP-poln. Tretji del namenimo pakirnemu kromatičnemu številu leksikografskega produkta grafov. Določimo njegovo spodnjo in zgornjo mejo ter izboljšano zgornjo mejo za primer, ko je prvi faktor v produktu izomorfen poti. V zadnjem delu se posvetimo učinkoviti odprti dominaciji produktov digrafov. Okarakteriziramo učinkovito odprto dominirane direktne in leksikografske produkte digrafov. Pri kartezičnem produktu okarakteriziramo tiste, kjer je prvi faktor usmerjena pot, usmerjen cikel ali zvezda z enim izvorom. Predstavimo tudi karakterizacijo učinkovito odprto dominiranega krepkega produkta, katerega temeljni graf obeh faktorjev je monocikličen graf.
Keywords:
pakirna množica
,
enolično največje pakiranje
,
dimenzija incidenčnosti
,
generator incidenčnosti
,
pakirno kromatično število
,
leksikografski produkt grafov
,
učinkovita odprta dominacija
,
usmerjeni grafi
,
produkti usmerjenih grafov
Place of publishing:
Maribor
Publisher:
[D. Božović]
Year of publishing:
2020
PID:
20.500.12556/DKUM-76594
UDC:
519.17(043.3)
COBISS.SI-ID:
39788035
NUK URN:
URN:SI:UM:DK:GXMBZODT
Publication date in DKUM:
27.11.2020
Views:
1563
Downloads:
195
Metadata:
Categories:
FNM
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:
BOŽOVIĆ, Dragana, 2020,
Nekatere s pakiranji povezane lastnosti grafov
[online]. Doctoral dissertation. Maribor : D. Božović. [Accessed 15 March 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=76594
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Licences
License:
CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:
http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:
The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:
12.06.2020
Secondary language
Language:
English
Title:
Some graph properties related to packings
Abstract:
In this dissertation, different problems related to packings are presented. The dissertation consists of four parts. In the first part, we focus on graphs with the unique packing of maximum cardinality. We first present several general properties for such graphs. Later two characterizations of trees with the unique maximum packing are presented. The second part introduces the concept of incidence dimension, which is directly related to the packing of a graph. We determine the formula for its calculation and prove that the problem of finding the incidence dimension of a graph is NP-complete in the general case. The third part is devoted to the packing chromatic number of the lexicographic product of graphs. Its lower and upper bounds are determined. The improved upper bound for the case where the first factor in the product is isomorphic to a path on
n
vertices is also presented. The last section deals with the efficient open domination of digraph products. We characterize the efficient open domination direct and lexicographic products of digraphs. Among Cartesian products, those whose first factor is a directed path, a directed cycle, or a single-source star are characterized. Characterization of the efficient open domination strong product digraphs for which the underlying graph of both factors is unicyclic is also presented.
Keywords:
packing set
,
unique maximum packing
,
incidence dimension
,
incidence generator
,
packing chromatic number
,
lexicographic product of graphs
,
efficient open domination
,
digraphs
,
products of digraphs
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