Particijska dimenzija grafov
diplomsko delo
Povzetek
Diplomsko delo obravnava particijsko dimenzijo grafov in je sestavljeno iz treh poglavij. V prvem poglavju bomo predstavili osnovne pojme iz teorije grafov in spoznali štiri najbolj znane produkte grafov, s poudarkom na kartezičnem produktu. Drugo poglavje bomo namenili predstavitvi dveh, za nas najpomembnejših dimenzij grafov. To sta metrična in particijska dimenzija grafov. Najprej bomo definirali metrično dimenzijo grafov in spoznali njene lastnosti. Nato se bomo posvetili particijski dimenziji grafov in njenim lastnostim. Pri obeh dimenzijah bomo za boljšo predstavitev podali tudi nekaj primerov. Na koncu tega poglavja pa si bomo ogledali tudi povezanost omenjenih dveh dimenzij. V zadnjem poglavju bomo definirali particijsko dimenzijo kartezičnega produkta grafov. Pogledali bomo zgornjo mejo te dimenzije, nato bomo spoznali njeno povezavo z metrično dimenzijo in na koncu navedli tudi dva aktualna odprta problema.
Ključne besede
matematika;grafi;rešljiva particija;množice;metrična dimenzija;kartezični produkti;diplomska dela;
Podatki
| Jezik: | Slovenski jezik |
|---|---|
| Leto izida: | 2011 |
| Izvor: | Maribor |
| Tipologija: | 2.11 - Diplomsko delo |
| Organizacija: | UM FNM - Fakulteta za naravoslovje in matematiko |
| Založnik: | [A. Tivadar] |
| UDK: | 51(043.2) |
| COBISS: |
18385672
|
| Št. ogledov: | 2321 |
| Št. prenosov: | 154 |
| Ocena: | 0 (0 glasov) |
| Metapodatki: |
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Ostali podatki
| Sekundarni jezik: | Angleški jezik |
|---|---|
| Sekundarni naslov: | THE PARTITION DIMENSION OF GRAPHS |
| Sekundarni povzetek: | The diploma paper discusses the partition dimension of graphs and consists of three chapters. In the first chapter the basic terms of the graph theory as well as the four most widely known products of graphs, with the emphasis on the Cartesian product, are presented. The second chapter is devoted to the presentation of the two for us most important dimensions of graphs. These are the metric and the partition dimension of graphs. First of all the metric dimension of graphs and it characteristics are presented. Afterwards the emphasis is on the partition dimension of graphs and its features. For a better understanding of both dimensions some examples are added. At the end of this chapter the connections between the two dimensions are presented. In the last chapter the partition dimension of the Cartesian product of graphs is defined. The upper bound of this dimension and the connections with the metric dimension are also shown. In the end two current open problems are stated. |
| Sekundarne ključne besede: | resolving partition;partition dimension of graphs;resolving set;metric dimension of graphs;the Cartasian product of graphs.; |
| URN: | URN:SI:UM: |
| Vrsta dela (COBISS): | Diplomsko delo |
| Komentar na gradivo: | Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo |
| Strani: | 48 f. |
| Ključne besede (UDK): | mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika; |
| ID: | 19278 |
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