Malnič, Aleksander ; Pisanski, Tomaž ; Žitnik, Arjana
Vsak končen graf na ▫$n$▫ vozliščih določa posebni ▫$(n-1)$▫-listni krovni graf, ki ga imenujemo klonski krov. Predstavimo več ekvivalentnih definicij in osnovnih lastnosti v zvezi s to zanimivo ...konstrukcijo. Tako npr. pokažemo, da je za ▫$k$▫ vsaj 2 klonski krov ▫$k$▫-povezanega grafa ▫$k$▫-povezan, da je klonski krov ravninskega grafa ravninski in da je klonski krov hamiltonskega grafa hamiltonski. Kar se tiče simetrijskih lastnosti, v večini primerov razumemo tudi strukturo grupe avtomorfizmov teh krovov. Posebej lepa lastnost je na primer, da se vsak avtomorfizem baznega grafa dvigne do avtomorfizma njegovega klonskega krova. Pokažemo tudi, da krovna projekcija klonskega krova na ustrezni ▫$2$▫-povezani bazni graf nikoli ni regularen krov, razen kadar je osnovni graf cikel.
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