The algorithmic complexity of signed domination in graphs

A two-valued function f defined on the vertices of a graph G (V, E), I : V -+ {-I, I}, is a signed dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every v E V, f(N[v]) 2: 1, where N(v] consists of v and every vertex adjacent to v. The of a signed dominating function is ICV) = L f( v), over all vertices v E V. The signed domination number of graph G, denoted /s(G), equals the minimum weight of a signed dominating function of G. The upper signed domination number of a graph G, denoted r.(G), equals the maximum weight of a minimal signed dominating function of G. In this paper we present a variety of algorithmic results on the complexity of signed and upper signed domination in graphs. "'Research supported in part by the South African Foundation for Research Development. tResearch supported in part by the University of Natal and the South African Foundation for Research Development. Austn:dasian Journal. of.· Combinatorics 1995), pp.101-112