On the computational complexity of upper fractional domination

Grant A. Cheston, G. Fricke, S.T. Hedetniemi, D. Pokrass Jacobs
1990 Discrete Applied Mathematics  
This paper studies a nondiscrete generalization of T(G), the maximum cardinality of a minimal dominating set in a graph G = (K:E). In particular, a real-valued the sum of the values assigned to the vertices in the closed neighborhood of u, N[o], is at least one, i.e., f (N[u]) 2 1. The weight of a dominating function f is f (V), the sum of all values f (u) for u E V, and T,(G) is the maximum weight over all minimal dominating functions. In this paper we show that: (1) Tf(G) is computable and is
more » ... always a rational number; (2) the decision problems corresponding to the problems of computing T(G) and Tf(G) are NP-complete; (3) for trees rf=r, which implies that the value of r, can be computed in linear time.
doi:10.1016/0166-218x(90)90065-k fatcat:colnl4yxejewtj32bgtdvkix7e