Various Bounds for Liar’s Domination Number
Let G = (V,E) be a graph. A set S ⊆ V is a dominating set if Uv∈S N[v] = V , where N[v] is the closed neighborhood of v. Let L ⊆ V be a dominating set, and let v be a designated vertex in V (an intruder vertex). Each vertex in L ∩ N[v] can report that v is the location of the intruder, but (at most) one x ∈ L ∩ N[v] can report any w ∈ N[x] as the intruder location or x can indicate that there is no intruder in N[x]. A dominating set L is called a liar’s dominating set if every v ∈ V (G) can be correctly...