Population structure has been proposed as one of the mechanism promoting cooperation. Until recently, most studies assumed that the interaction network can be described by a regular graph. Recently, Ohtsuki et al. [1] have shown for a number of other interaction topologies that selection favours cooperation (i.e. the fixation probability of a single cooperator is higher than the fixation probability of a neutral mutant) in the prisoners dilemma game if the benefit (b) of the altruistic act divided by its cost (c) exceeds the average number of neighbours (k), that is, if b=c > k. They found this relation to be approximately valid in populations of different structure, in which interaction topology is described variously by regular, random regular, random, or scale-free graphs. Similarly, Santos et al. [4] have shown that the heterogeneous degree distribution of these other types of graphs generally facilitate the dominance of cooperative behaviour. Previous studies [1], [4], [5] have assumed that the graph is static during evolution. This assumption implies that a newborn individual (or accepted strategy-by-imitation) in a given position interacts with exactly the same individuals that were connected to every preceding individual at this position. Some recent papers studied the evolution of cooperation on dynamical networks. They either studied the fixation probability of a single cooperator among defectors in the case when graph dynamics is much faster than dynamics of evolution [2], or if the relative speed of graph and evolutionary dynamics were waried systematically they assumed that cooperators and defectors were in the same fraction initially in the population [3], [4]. Here we investigate how sensitive is the fixation probability of a single cooperator to the network dynamics, if dynamics is slow relative to the evolution.