On the computational complexity of upper distance fractional domination

Let. n ?: 1 be an integer and lei G = (V, E) be a graph. In this paper we study a non discrete generalization of l'n(G), the maximum cardinality of a minimal n-dominating sei in G. A real-valued function f : V -t [0,1] is n-dominating if for each v E V, the sum of the values assigned to the vertices in the closed n-neighbourhood of v, Nn[v], is at least one, i.e., f(Nn [ll]) ?: 1. The weight of an n-dominating function f is J(1I), the sum of all values J( v) for v E if, and l' nj( G) is the maxinium weight over all minimal n-dominating functions. We show that the decision problems corresponding to the problems of computing l'n(G) and l'nj(G) are NP-complete, generalising the result of Cheston, Fricke, lIedetniemi and Jacobs for the case n = 1.