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Title:
CELOŠTEVILSKE DOMINACIJSKE INVARIANTE NA GRAFIH
Authors:
ID
Komovec, Luka
(Author)
ID
Brešar, Boštjan
(Mentor)
More about this mentor...
Files:
UNI_Komovec_Luka_2009.pdf
(501,60 KB)
MD5: 7E3466DB81BD1165BCD4DA9A9499F507
PID:
20.500.12556/dkum/fe0fef5d-2538-49d9-a751-d3bb9e7253bc
Language:
Slovenian
Work type:
Undergraduate thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
Naj bo Y podmnožica množice celih števil in G = (V,,E) graf. Funkcija, ki vsakemu vozlišču priredi neko vrednost iz množice Y, tako da je seštevek vrednosti v soseščini vsakega vozlišča vsaj 1, se imenuje celoštevilska dominacijska funkcija grafa G. Vrednost celoštevilske dominacijske funkcije v poljubni podmnožici S množice V definiramo kot seštevek vrednosti v vsakem vozlišču iz S. Teža celoštevilske dominacijske funkcije je vrednost funkcije v množici vozlišč V. Poiskati želimo po teži najmanjšo celoštevilsko dominacijsko funkcijo grafa G. V tem delu so predstavljene variacije različnih celoštevilskih dominacij, kot so {k}-dominacija, k-kratna dominacija, predznačena dominacija in minus dominacija, ki jih obravnavamo na razredih grafov kot so poti, cikli, pahljače, kolesa, ponve in trampolini. Podan je algoritem, ki v linearnem času reši problem L-dominacije na strogo tetivnih grafih. Prav tako je podana časovna zahtevnost izračuna naštetih celoštevilskih dominacijskih invariant za razrede dualno tetivnih, dvojno tetivnih in ravninskih grafov. Na koncu je na podoben način predstavljena 2-mavrična dominacija.
Keywords:
celoštevilska dominacija
,
k-kratna dominacija
,
predznačena dominacija
,
minus dominacija
,
{k}-dominacija
,
2-mavrična dominacija
,
tetivni grafi
,
dualno tetivni grafi
,
dvojno tetivni grafi
,
strogo tetivni grafi
Place of publishing:
Maribor
Publisher:
[L. Komovec]
Year of publishing:
2009
PID:
20.500.12556/DKUM-10406
UDC:
51(043.2)
COBISS.SI-ID:
16946440
NUK URN:
URN:SI:UM:DK:ZWDXKEUX
Publication date in DKUM:
17.06.2009
Views:
2582
Downloads:
205
Metadata:
Categories:
FNM
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:
KOMOVEC, Luka, 2009,
CELOŠTEVILSKE DOMINACIJSKE INVARIANTE NA GRAFIH
[online]. Bachelor’s thesis. Maribor : L. Komovec. [Accessed 23 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=10406
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Secondary language
Language:
English
Title:
INTEGER DOMINATION INVARIANTS ON GRAPHS
Abstract:
Let Y be a set of integers. An integer dominating function of graph G = (V,,E) is a function that sets a value from Y to every vertex from V in such way that sum of values from neighbourhood of every vertex is at least 1. Let S be a subset of V. The value of an integer dominating function in S is defined as the sum of its values over vertices from S. The weight of integer dominating function is its value in V. The goal is to find a minimum weight integer dominating function of graph G. In this work we present the variation of integer domination such as {k}-domination, k-tuple domination, signed domination, and minus domination numbers which we study on classes of graphs such as paths, cycles, fans, wheels, pans and suns. We give the algorithm that solves L-domination in linear time on strongly chordal graphs. We also give complexity results for the mentioned integer domination invariants on dually chordal, doubly chordal, and planar graphs. At the end a 2-rainbow domination is presented in a similar way.
Keywords:
integer domination
,
k-tuple domination
,
signed domination
,
minus domination
,
{k}-domination
,
2-rainbow domination
,
chordal graphs
,
dually chordal graphs
,
doubly chordal graphs
,
strongly chordal graphs
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