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Teorija grafov. Del 2, Algebraična teorija grafov
Marušič, Dragan
Ukvarjamo se s hamiltonskimi in Cayleyjevimi lastnostmi po točkah simetričnih grafov. Dokažemo, da ima vsak po točkah simetričen graf reda ▫$2p^2$▫ (kjer je ▫$p$▫ praštevilo) hamiltonov cikel. Eden ...važnejših rezultatov je tudi izrek, ki pravi, da je vsak simetrični graf reda ▫$2p$▫, kjer je ▫$p\equiv ({\rm mod}4)$▫, oziroma reda ▫$p, p^2$▫ in ▫$p^3$▫ nujno Cayleyjev graf. Za vsako naravno število ▫$n$▫ deljivo s ▫$p^4$▫ konstruiramo po točkah simetričen graf, ki ni Cayleyjev. Na koncu strnemo še nekaj rezultatov iz simetričnih grafov ter omenimo možne poti za rešitev nekaterih nerešenih problemov iz tega področja matematike.
Type of material - research report
Publication and manufacture - Ljubljana : Inštitut za matematiko, fiziko in mehaniko, 1983
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