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13.
Exotic ▫$n$▫-universal graphs
Parsons, Torrence Douglas ; Pisanski, Tomaž
Graf je ▫$n$▫-univerzalni graf, če vsebuje kot inducirani podgraf primerek vsakega grafa na ▫$n$▫ točkah. Pokazano je, da za vsako pozitivno število ▫$n>1$▫ obstaja ▫$n$▫-univerzalni graf ▫$G$▫ na ...▫$4^n-1$▫ točkah z lastnostmi: ▫$G$▫ je ▫$(v,k,\lambda)$▫-graf, ▫$G$▫ in njegov komplement ▫$\overline{G}$▫ sta 1-tranzitivna v smislu W.T.Tutta in imata diameter 2. Grupa avtomorfizmov grafa ▫$G$▫ je tranzitivna permutacijska grupa ranga 3, t.j. deluje tranzitivno na (1) točkah ▫$G$▫, (2) urejenih parih ▫$uv$▫ sosednjih točk grafa ▫$G$▫ in (3) urejenih parih ▫$xy$▫ nesosednjih točk grafa ▫$G$▫.
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