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Partitioning the vertex set of ▫$G$▫ to make ▫$G \Box H$▫ an efficient open domination graph [Elektronski vir]
Kraner Šumenjak, Tadeja ...
Graf imenujemo učinkovito odprto dominiran, če zanj obstaja podmnožica vozlišč, katerih odprte okolice porajajo particijo množice vseh vozlišč. Karakteriziramo take grafe ▫$G$▫, da je kartezični ...produkt ▫$G \Box H$▫ učinkovito odprto dominiran v primerih, ko je ▫$H$▫ poln graf na vsaj treh vozliščih ali poln dvodelni graf. V obeh primerih karakterizacija temelji na obstoju določenega tipa šibke particije množice ▫$V(G)$▫. Za drevesa je, ko je ▫$H$▫ poln graf na vsaj treh vozliščih, karakterizacija konstrukcijska. Prav tako med kartezičnimi produkti ▫$G \Box H$▫ karakteriziramo posebne tipe učinkovito odprto dominiranih grafov, ko je ǂ$H$ǂ 5-cikel ali 4-cikel.
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