FMF, Mathematical Library, Lj. (MAKLJ)
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Spektralna metoda za določanje pasovnosti grafa : diplomsko delo : Prešernova nagrada študentomJuvan, MartinV diplomskem delu je obravnavan problem določanja pasovnosti grafov. Najprej je vpeljana posplošitev pasovnosti, ki jo imenujemo ▫$p$▫-pasovnost. Opravljen je pregled važnejših rezultatov s tega ... področja, izpeljanih pa je tudi nekaj povezav med različnimi pasovnostmi. V nadaljevanju je vpeljana še Laplaceova matrika grafa, dokazane so nekatere znane lastnosti te matrike in njenega spektra, poudarek pa je predvsem na prikazu pomembnosti druge najmanjše lastne vrednosti ▫$\lambda_2$▫ te matrike. Iz izpeljanih lastnosti spektra Laplaceove matrike dobimo zanimive "spektralne" ocene za nekatere ▫$p$▫-pasovnosti, ▫$p\in\{1,2,\infty\}$▫. Omenjena je tudi prerezna pasovnost. Prikazan je še hevristični algoritem za iskanje približka k optimalni označitvi grafa s pomočjo lastnih vrednosti ▫$\lambda_2$▫ pripadajočega lastnega vektorja ▫$x^{(2)}$▫. Opravljena je kratka analiza napake algoritma, iz izračunanih primerov pa ugotovimo, da je njegovo obnašanje zadovoljivo.Type of material - undergraduate thesisPublication and manufacture - Ljubljana : [M. Juvan], 1989Language - slovenianCOBISS.SI-ID - 3534937
Author
Juvan, Martin
Other authors
Mohar, Bojan, 1956-
Topics
matematika |
teorija grafov |
pasovnost |
Laplaceova matrika grafa |
spektralne ocene |
hevristični algoritem |
bandwidth |
cutwidth |
Laplacian matrix |
spectral bounds |
heuristic algorithm
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Skladišče-Jadranska 21 0000010668/0000000394 0000000001 Skladišče-Jadranska 21 10668/394 1 |
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Juvan, Martin | 11220 |
Mohar, Bojan, 1956- | 01931 |
Source: Personal bibliographies
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