Connectivity and some other properties of generalized Sierpiński graphs
Klavžar, Sandi ; Zemljič, Sara Sabrina
Če je ▫$G$▫ graf in ▫$n$▫ pozitivno celo število, potem je posplošeni graf Sierpińskega ▫$S_G^n$▫ fraktalen graf, ki kot gradnike uporablja graf ▫$G$▫. Konstrukcija grafov ▫$S_G^n$▫ posplošuje ...klasične grafe Sierpińskega ▫$S_p^n$▫, kjer vlogo grafa ▫$G$▫ igra polni graf ▫$K_p$▫. Podana je eksplicitna formula za število povezanih komponent ▫$S_G^n$▫. Dokazano je, da je povezanost (po povezavah) grafa ▫$S_G^n$▫ enaka povezanosti (po povezavah) grafa ▫$G$▫. Nadalje je dokazano, da ▫$S_G^n$▫ vsebuje ▫$1$▫-faktor natanko tedaj, ko $G$ vsebuje ǂ$1$ǂ-factor. Obravnavana je tudi hamiltonskost posplošenih grafov Sierpińskega.
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