Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures Original Research Article

A function f defined on the vertices of a graph G=(V,E),f : V→{−1,0,1} is a minus dominating function if the sum of its values over any closed neighborhood is at least one. The weight of a minus dominating function is f(V)=∑v∈V f(v). The minus domination number of a graph G, denoted by γ−(G), equals the minimum weight of a minus dominating function of G. In this paper, a sharp lower bound on γ− of k-partite graphs is given. The special case k=2 implies that a conjecture proposed by Dunbar et al. (Discrete Math. 199(1999) 35) is true.