Nowadays, wireless local-area networks (WLANs) are widely deployed in residential and commercial areas. The coverage quality is essential to users. The full coverage appears to be one of the most crucial problems to be considered during the network and access-point/router deployment (placement). We formulate the light-of-sight (LoS) coverage problem using the visibility-graph framework. In this work, for arbitrary multiply-connected or simply-connected polygonal/prismatic fields-of-interest subject to an arbitrary link-range restriction, we investigate how the full LoS coverage can be achieved by a minimum number of access-points/routers. Based on the new mathematical lemmas we derive, we design a novel graph-theoretical approach accordingly. Our proposed new scheme can be deemed the first-ever systematic approach to the best of our knowledge. Our proposed new approach is also evaluated in terms of the coverage efficiency, the number of access-points/routers, and the peak link-distance ratio for full LoS coverage in comparison with the existing solution to the art gallery problem.