Cockayne, E.J.Fricke, G.Hedetniemi, S.T.Mynhardt, C.M.2010-03-042010-03-0419902010-03-04http://hdl.handle.net/1828/2320A dominating function for a graph is a function from its vertex set into the unit interval so that the sum of function values taken over the closed neighbourhood of each vertex is at least one. We prove that any graph has a positive minimal dominating function and begin an investigation of the question: When are convex combinations of minimal dominating functions themselves minimal dominating?entechnical reports (mathematics and statistics)Technical ReportDepartment of Mathematics and Statistics