Vertex-removal in α-domination
Nader Jafari Rad, Lutz Volkmann · Filomat · 2012
Let G = (V, E) be any graph without isolated vertices. For some ? with 0 < ? ? 1 and a dominating set S of G, we say that S is an ?-dominating set if for any v ? V ? S, |N(v) ? S| ? ?|N(v)|. The cardinality of a smallest ?-dominating set of G is called the ?-domination number of G and is denoted by ?? (G). In this paper, we study the effect of vertex removal on ?-domination.