Če je ▫$G$▫ graf, potem je zaporedje vozlišč ▫$v_1,\dots,v_m$▫ zaporedje zaprtih okolic, če za vse ▫$2\le i \le m$▫ velja ▫$N[v_i]\not\subseteq \cup_{j=1}^{i-1}N[v_j]$▫ in je zaporedje odprtih ...okolic, če za vse ▫$2\le i \le m$▫ velja ▫$N(v_i)\not\subseteq \cup_{j=1}^{i-1}N(v_j)$▫. Dolžina najdaljšega zaporedja zaprtih (odprtih) okolic je Grundyjevo (Grundyjevo celotno) dominantno število grafa ▫$G$▫. V tem članku vpeljemo dva podobna koncepta, v katerih je zahteva za soseščine spremenjena v ▫$N(v_i)\not\subseteq \cup_{j=1}^{i-1}N[v_j]$▫ ali v ▫$N[v_i]\not\subseteq \cup_{j=1}^{i-1}N(v_j)$▫. V prvem primeru vzpostavimo močno povezavo s številom ničelne prisile grafa, medtem ko v drugem primeru določimo računsko zahtevnost odločitvenega problema. Raziskujemo tudi razmerja med vsemi štirimi koncepti in razpravljamo o njihovih računskih zahtevnostih.
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