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Title:Razdaljno magično označevanje grafov
Authors:ID Švaljek, Nika (Author)
ID Tepeh, Aleksandra (Mentor) More about this mentor... New window
Files:.pdf UNI_Svaljek_Nika_2013.pdf (1,86 MB)
MD5: EAA49A31490E488D4BAF97E38E3F753F
PID: 20.500.12556/dkum/0f9b2b14-3bb5-4f31-9f67-bf9bd2503909
 
Language:Slovenian
Work type:Undergraduate thesis
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:Razdaljno magično označevanje grafa je bijekcija f : V -> {1, 2,...,n}, z lastnostjo, da obstaja taka konstanta k, da za vsako vozlišče x grafa velja, f(x_1)+f(x_2)+...+f(x_j)= k, kjer je y_i (i = 1,...,j) iz odprte okolice vozlišča x. Diplomsko delo obravnava razdaljno magično označevanje polnih dvodelnih in polnih tridelnih grafov. V prvem poglavju so predstavljeni osnovni pojmi teorije grafov s poudarkom na polnih večdelnih grafifih in barvanjih grafa. V drugem delu najprej predstavimo potreben pogoj za obstoj razdaljno magičnega označevanja. Glavni rezultat tega poglavja je karakterizacija polnih dvodelnih in polnih tridelnih grafov, za katere obstaja razdaljno magično označevanje. Delo zaključimo s seznamom različnih družin grafov, za katere razdaljno magično označevanje ne obstaja.
Keywords:teorija grafov, razdaljno magično označevanje, k - regularni graf, večdelni graf, polni dvodelni graf, polni tridelni graf
Place of publishing:Maribor
Publisher:[N. Švaljek]
Year of publishing:2013
PID:20.500.12556/DKUM-39769 New window
UDC:51(043.2)
COBISS.SI-ID:19770376 New window
NUK URN:URN:SI:UM:DK:D6CDCLJU
Publication date in DKUM:27.03.2013
Views:2742
Downloads:194
Metadata:XML DC-XML DC-RDF
Categories:FNM
:
ŠVALJEK, Nika, 2013, Razdaljno magično označevanje grafov [online]. Bachelor’s thesis. Maribor : N. Švaljek. [Accessed 19 March 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=39769
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Secondary language

Language:English
Title:Distance magic labelings of graphs
Abstract:A magic distance labeling is a bijection f : V -> {1, 2,...,n} with the property that there is a constant k such that f(y_1)+f(y_2)+...+f(y_j) = k for every vertex x, where y_i (i=1,...,j) is the set of vertices adjacent to x. The graduation thesis investigates magic distance labelings of complete bipartite and complete tripartite graphs. In the first chapter basic concepts of graph theory are presented with the emphasis on complete multipartite graphs and colourings of graphs. In the second part we first present a necessary condition for the existence of a magic distance labeling. The main result in this chapter is a caracterization of complete bipartite and complete tripartite graphs that admit magic distance labeling. We conclude by listing various families of graphs, all of which have no distance magic labeling.
Keywords:graph theory, magic distance labeling, k - regular graphs, multipartite graphs, complete bipartite graphs, complete tripartite graphs


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