In WSN, it is not often desirable to use the GPS technology. Indeed, the use of GPS is expensive and may reduce the overall network performance. Moreover, indoor reception of the GPS signal is not possible. The Link Quality Indicator (LQI) is defined in the 802.15.4 standard, but its context of use is not specified in this standard. Some works on the LQI, few of which are field experiments, have shown that the LQI decreases as the distance increases. However, the challenge of clustering mechanisms is to form the smallest number of clusters by maximizing distances separating cluster heads to provide an efficient cover of the network and also minimizes the cluster overlaps. This reduces the amount of channel contention between clusters, and also improves the efficiency of algorithms that run at the level of the cluster heads. Therefore we propose an analytical model based on the use of the LQI in order to derive an optimally one-dominating set in which the smaller distance separating two cluster heads is improved