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13.
Nonorientable embeddings of groups
Pisanski, Tomaž ; White, Arthur T.
Študiramo vložitve Cayleyjevih grafov n neorientabilne ploskve. Izpeljanih je nekaj spodnjih in zgornjih mej za neorientabilni rod Abelovih in Hamiltonskih grup. V primeru, ko zgornja in spodnja meja ...sovpadata, je izračunan neorientabilni rod. Naj bo npr. ▫$A = \mathbb Z_{m_1} \times \mathbb Z_{m_2} \times \ldots \times \mathbb Z_{m_r}$▫, kjer ▫$m_{i+1}|m_i$▫ za ▫$1 \le i\le r-1$▫. Če 4 deli ▫$m_i$▫, ▫$r \ge 3$▫ in je ▫$m_r$▫ lih, ▫$m_r \ge 5$▫, potem ima ▫$A$▫ neorientabilni rod ▫$2+(r-2)|A|/2$▫. V nekaterih primerih to metodo uporabimo na orientabilnih vložitvah. Na primer, če ima Abelov faktor ▫$A$▫ v hamiltonski grupi ▫$H$▫ rang ▫$r\ge 6$▫, potem sta tako orientabilni kot neorientabilni rod ▫$H$▫ določena, razen ko je ▫$|A|$▫ liho ali ko je ▫$m_r=3$▫.
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