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<div class="csl-entry">Seitz, G. (2011). <i>Analysis of various parameters in labelled trees and tree-like structures</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-53297</div>
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We analyse various parameters in labelled trees (i.e. in trees in which the nodes are labelled with distinct integers) and, more generally, in labelled tree-like graph structures. In trees, we consider two parameters which have already been extensively studied in finite sequences (especially in permutations), namely the number of inversions and the number of local minima. We analyse the behaviour of these quantities in random trees of various labelled tree families. Moreover, we consider a class of graphs known as k-trees. These are graphs with a tree-like structure, which can be constructed by a certain randomised graph evolution process, and which can be seen as a simple model for the growth of complex networks. In these graphs, we study parameters which have already been analysed in ordinary trees, namely the number of ancestors and descendants of nodes and the degree distribution. By the use of generating functions we obtain to a large extent very precise results on the exact distribution of these quantities if the size of the considered random objects is fixed. Apart from that, we can characterize the limiting behaviour of each of these quantities as the size of the considered objects tends to infinity.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
markierte Bäume
de
dc.subject
baumartige Strukturen
de
dc.subject
k-dimensionale Bäume
de
dc.subject
Inversionen
de
dc.subject
Vorfahren
de
dc.subject
Nachkommen
de
dc.subject
Gradverteilung
de
dc.subject
lokale Minima
de
dc.subject
labelled trees
en
dc.subject
tree-like structures
en
dc.subject
k-trees
en
dc.subject
inversions
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dc.subject
ancestors
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dc.subject
descendants
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dc.subject
degree distribution
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dc.subject
local minima
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dc.title
Analysis of various parameters in labelled trees and tree-like structures
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dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Georg Seitz
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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dc.contributor.assistant
Fischer, Ilse
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tuw.publication.orgunit
E104 - Institut für Diskrete Mathematik und Geometrie