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13.
Dimenzija grafov : magistrsko delo
Šemrl, Melita
Magistrsko delo obravnava dimenzijo grafov. V drugem poglavju predstavimo definicijo dimenzije grafov in podamo nekaj primerov grafov z znanimi dimenzijami. Opisana je koordinatna vložitev grafa, s ...katero lahko določimo, kolika je dimenzija nekaterih grafov. Pokazano je, kako je separirajoča družina ekvivalenčnih relacij na množici točk grafa povezana z dimenzijo grafa, in kako je dimenzija grafa povezana s kromatičnim indeksom. Podanih je nekaj trditev o dimenziji grafov, ki jih dobimo z različnimi operacijami. Pokazano pa je tudi, kako je dimenzija grafa odvisna od števila točk grafa in od največje stopnje točk grafa. V tretjem poglavju predstavimo posebne vektorje, s katerimi pokažemo, kako je dimenzija grafov omejena navzdol. Posebno pozornost namenimo dimenziji poti, ciklov in hiperkock. Četrto poglavje obravnava osnovni metodi za ocenitev dimenzije vsote dveh kopij istega grafa, ki vključujeta največjo stopnjo točk grafa in kromatično število grafa. V posebnem primeru se posvetimo dimenziji vsote dveh polnih grafov, kjer pristopimo z matrikami, ki imajo lastnost pokritja. Magistrko delo zaključimo s kratkim pregledom še drugih znanih rezultatov in sorodnimi koncepti.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Ptuj : [M. Šemrl], 2005
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