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On vertex symmetric digraphs : a thesis submitted for the degree of Doctor of PhilosophyMarušič, DraganV prvem delu obravnavamo strukturo točkovno tranzitivnih usmerjenih grafov, še posebej njihove grupe avtomorfizmov. Dokažemo, da ima vsak točkovno tranzitiven usmerjen graf reda ▫$p^k$▫ ali ▫$mp$▫ ... (kjer je ▫$p$▫ praštevilo ▫$k\ge 1$▫ in ▫$m\le p$▫) avtomorfizem čigar vse orbite so dolžine ▫$p$▫. Karakteriziramo še točkovno tranzitivne grafe reda ▫$2p$▫, če ▫$2p-1$▫ ni kvadrat nekega sestavljenega števila. Dokažemo tudi, da so točkovno tranzitivni usmerjeni grafi reda ▫$p^k \; (k\le 3)$▫ Cayleyjevi usmerjeni grafi. V drugem delu obravnavamo hamiltonske lastnosti točkovno tranzitivnih grafov. Dokažemo, da je vsak povezan točkovno tranzitiven graf reda ▫$p^2,\; p^3$▫ ali ▫$3p$▫ (▫$p$▫ je praštevilo) hamiltonski in da ima vsak povezan točkovno tranzitiven graf reda ▫$4p$▫ ali ▫$5p$▫, kjer je ▫$p$▫ praštevilo, hamiltonsko pot. Pokažemo tudi, da je vsak povezan Cayleyjev graf z najmanj tremi točkami poldirektnega produkta ciklične grupe praštevilskega reda z Abelovo grupo lihega reda hamiltonski.Type of material - dissertationPublication and manufacture - Reading : [D. Marušič], 1981Language - englishCOBISS.SI-ID - 563289
Author
Marušič, Dragan
Other authors
Nash-Williams, C.
Topics
matematika |
teorija grafov |
simetični usmerjeni grafi |
Cayleyjevi grafi |
Hamiltonov graf |
Hamiltonova pot |
mathematics |
graph theory |
vertex symmetric digraphs |
graphs |
Cayley graphs |
Hamilton circuits |
Lovász's conjecture |
groups |
Hamilton paths
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FMF and IMFM, Mathematical Library, Ljubljana | Ljubljana | MAKLJ |
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Database name | Field | Year |
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Marušič, Dragan | 02887 |
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