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Title:
DISKRIMINATORNE KODE V DVODELNIH GRAFIH
Authors:
ID
Kolarič, Denis
(Author)
ID
Kovše, Matjaž
(Mentor)
More about this mentor...
Files:
UNI_Kolaric_Denis_2010.pdf
(626,67 KB)
MD5: D3D8768A6CFB38C5F3704EFA53A0FF23
PID:
20.500.12556/dkum/7c032d1b-ef8b-4290-ac73-e1971d07858c
Language:
Slovenian
Work type:
Undergraduate thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
V uvodnem poglavju predstavimo osnovne definicije iz teorije grafov, ki jih potrebujemo v nadaljevanju in povemo še nekaj o kodah v grafih. V naslednjem poglavju definiramo diskriminatorne kode, podamo nekaj primerov in dokažemo spodnjo in zgornjo mejo za moč minimalne diskriminatorne kode izražene glede na število atributov. V tretjem poglavju pokažemo povezavo med diskriminatornimi in identifikacijskimi kodami v hiperkockah. V četrtem poglavju obravnavamo diskriminatorne kode v drevesih in opišemo algoritem linearne časovne zahtevnosti glede na število vozlišč drevesa, ki za dano drevo poišče minimalno diskriminatorno kodo v drevesu in njegovo delovanje prikažemo na primeru. V zadnjem poglavju podamo za vnaprej podano število atributov konstrukcijo dvodelnih ravninskih grafov brez dvojčkov, ki imajo največje število posameznikov in pokažemo povezavo z ravninskimi triangulacijami.
Keywords:
identifikacijska koda
,
diskriminatorna koda
,
dvodelni graf
,
posameznik
,
atribut
,
hiperkocka
,
drevo
,
algoritem
,
ravninski graf
Place of publishing:
Maribor
Publisher:
[D. Kolarič]
Year of publishing:
2010
PID:
20.500.12556/DKUM-16104
UDC:
51(043.2)
COBISS.SI-ID:
17925896
NUK URN:
URN:SI:UM:DK:TH2HL8XH
Publication date in DKUM:
22.10.2010
Views:
2959
Downloads:
237
Metadata:
Categories:
FNM
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:
KOLARIČ, Denis, 2010,
DISKRIMINATORNE KODE V DVODELNIH GRAFIH
[online]. Bachelor’s thesis. Maribor : D. Kolarič. [Accessed 12 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=16104
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Secondary language
Language:
English
Title:
DISCRIMINATING CODES IN BIPARTITE GRAPH
Abstract:
In the preliminaries we give necessary definitions from graph theory and codes in graphs that we need later. In the next chapter we define discriminating codes, give some examples and show lower and upper bounds for the size of minimal discriminating codes, expressed in terms of the number of atributes of a given graph. In the third chapter we show the relation between discriminating and identifying codes in hypercubes. In the fourth chapter discriminating codes in trees are treated and linear time algorithm for finding a minimal discriminating code in a tree is given and ilustrated with an example. In the last chapter we describe all bipartite planar graphs without twins with a property, that for a given number of atributes they have the maximal number of individuals, and we show their relation with planar triangulations.
Keywords:
identifying code
,
discriminating code
,
bipartite graph
,
individual
,
atribute
,
hypercube
,
tree
,
algorithm
,
planar graph
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