The annihilation number does not bound the 2-domination number from the above
Yue, Jun ...
▫$2$▫-dominantno število ▫$\gamma_2(G)$▫ grafa ▫$G$▫ je moč najmanjše množice▫ $S\subseteq V(G)$▫, tako da je vsako vozlišče iz ▫$V(G)\setminus S$▫ sosedno z vsaj dvema vozliščema iz ▫$S$▫. Število ...uničenja ▫$a(G)$▫ grafa ▫$G$▫ je največje naravno število ▫$k$▫, tako da je vsota prvih ▫$k$▫ členov nepadajočega zaporedja stopenj grafa ▫$G$▫ kvečjemu število njegovih povezav. Postavljena je bila domneva, da neenakost ▫$\gamma_2(G) \leq a(G) +1$▫ velja za vsaj povezan graf ▫$G$▫. Domneva je bila so sedaj med drugim potrjena za grafe z minimalno stopnjo ▫$3$▫, za drevesa in za bločne grafe. V tem članku ovržemo domnevo tako, da dokažemo, da je lahko ▫$2$▫-dominantno število poljubno večje od števila uničenja. Na pozitivni strani pa dokažemo, da domnevana meja velja za velik podrazred dvodelnih, povezanih kaktusov, s čimer posplošimo rezultat Jakovca iz [Discrete Appl. Math. 260 (2019) 178-187].
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