Naj bo ▫$G$▫ graf. Tedaj je ▫$k$▫-dominacijski graf ▫$D_k(G)$▫ grafa ▫$G$▫ definiran takole: Njegova vozlišča so dominantne množice grafa ▫$G$▫ moči kvečjemu ▫$k$▫, dve taki množici sta sosedni, če ...se razlikujeta za natanko eno dodano ali zbrisano vozlišče. Graf je dominacijski graf, če je izomorfen ▫$D_k(G)$▫ za nek graf ▫$G$▫ in neko pozitivno celo število ▫$k$▫. V članku odgovorimo na vprašanje avtorjev Haas in Seyffarth s tem, ko dokažemo, da v razredu grafov brez izoliranih vozlišč velja, da če je ▫$G$▫ graf reda ▫$n\ge 2$▫, za katerega velja ▫$G\cong D_k(G)$▫, potem je ▫$k=2$▫ in ▫$G \cong K_{1,n-1}$▫ za nek ▫$n\ge 4$▫. Dokazano je tudi, da za fiksen ▫$r$▫ obstaja le končno mnogo ▫$r$▫-regularnih, povezanih dominacijskih grafov povezanih grafov. V posebnem, cikla ▫$C_6$▫ in ▫$C_8$▫ sta edina dominacijska grafa v razredu ciklov. Dobljenih je tudi nekaj rezultatov o redu dominacijksih grafov.
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