Abstract
An upper bound is established on the parameter Γ− (G) for a cubic graphG and two infinite families of 3-connected graphs Gk, Gk* are constructed to show that the bound is sharp and, moreover, the difference Γ−(Gk*)-γs(Gk*) can be arbitrarily large, where Γ−(Gk*) and γs(Gk*) are the upper minus domination and signed domination numbers of Gk*, respectively. Thus two open problems are solved.
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