On Jacobian group and complexity of ▫$I$▫-graph ▫$I(n, k, l)$▫ through Chebyshev polynomials
Mednykh, Ilya
Obravnavamo družino ▫$I$▫-grafov ▫$I(n, k, l)$▫, ki predstavlja posplošitev razreda posplošenih Petersenovih grafov. V tem članku podamo novo metodo štetja v Jacobijevi grupi ▫$I$▫-grafa ▫$I(n, k, ...l)$▫. Pokažemo, da je minimalno število generatorjev grupe Jac▫$(I(n, k, l))$▫ najmanj dve in največ ▫$2k + 2l - 1$▫. Podamo tudi zaključeno formulo za število vpetih dreves grafa ▫$I(n, k, l)$▫, izraženo s polinomi Čebiševa. Raziskujemo nekaj aritmetičnih lastnosti tega števila in njegovo asimptotično vedenje.
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