diplomsko delo
Andreja Šereg (Author), Marko Jakovac (Mentor)

Abstract

V diplomskem delu so predstavljeni grafi Sierpińskijevega tipa, in sicer grafi Sierpińskega S(n, k), grafi trikotnikov Sierpińskega S_n, regularni grafi Sierpińskega S^+(n, k) in S^++(n, k) in posplošeni grafi trikotnikov Sierpińskega S[n, k]. Prikazane so natančne risbe grafov S(n, k), S^+(n, k) in S^++(n, k). Za S^+(n, k) in S^++(n, k) je dokazano, da so te risbe optimalne. Določeno je število po povezavah disjunktnih Hamiltonovih poti in Hamiltonovih ciklov v grafih S(n, k), S^+(n, k) in S^++(n, k). Dokazano je, da so grafi S[n, k] Hamiltonovi. Raziskana je vozliščna linearna pogozdenost grafov S(n, k), S^+(n, k), S^++(n, k) in S[n, k]. Podano je še {P_r}-prosto kromatično število grafov S_n, S(n, k), S^+(n, k) in S^++(n, k), za r % {3, 4}.

Keywords

matematika;grafi Sierpińskega;grafi trikotnikov Sierpińskega;prekrižno število;hamiltonskost;vozliščna linearna pogozdenost;diplomska dela;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [A. Šereg]
UDC: 51(043.2)
COBISS: 20061448 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Some generalizations of Sierpiński graphs
Secondary abstract: In this graduation thesis Sierpiński-like graphs, namely Sierpiński graphs S(n, k), Sierpiński gasket graphs S_n, regular Sierpiński graphs S^+(n, k) and S^++(n, k) and generalized Sierpiński gasket graphs S[n, k] are presented. Explicit drawings of graphs S(n, k), S^+(n, k) and S^++(n, k) are shown and proved to be optimal for S^+(n, k) and S^++(n, k). The numbers of edge disjoint Hamiltonian paths and Hamiltonian cycles in S(n, k), S^+(n, k) and S^++(n, k) are determined. Graphs S[n, k] are proven to be Hamiltonian. Vertex linear arboricity of S(n, k), S^+(n, k), S^++(n, k) and S[n, k] is studied. {Pr}-free cromatic number of S_n, S(n, k), S^+(n, k) and S^++(n, k) for r % {3, 4} is given.
Secondary keywords: Sierpiński graph;Sierpiński gasket graph;regular Sierpiński graph;generalized Sierpiński gasket graph;crossing number;Hamiltonicity;path t-coloring;vertex linear arboricity;{P_r}-free chromatic number;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: IX, 63 f.
ID: 8726882