A new generalization of generalized Petersen graphs [Elektronski vir]
Jasenčáková, Katarína ; Jajcay, Robert ; Pisanski, Tomaž
Obravnavamo novo družino kubičnih grafov, ki jo imenujemo grupno deljivi posplošeni Petersenovi grafi (▫$SGP$▫-grafi), in je, tako po definiciji kot po lastnostih, zelo podobna družini posplošenih ...Petersenovih grafov. V članku se osredotočamo na določitev algebraičnih lastnosti grafov naše nove družine. Iščemo visoko simetrične grafe, t.j. grafe z velikimi grupami avtomorfizmov, in točkovno- ali ločno-tranzitivne grafe. Posebej, podamo aritmetične pogoje za določitvene parametre, ki zagotavljajo, da so grafi s temi parametritočkovno-tranzitivni ali Cayleyjevi, in poiščemo primer ločno-tranzitivnega ▫$SGP$▫-grafa,ki ni niti ▫$CQ$▫ graf Fenga in Wanga niti posplošeni Petersenov graf.
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