Comparability Graphs and Digital Topology

D. Nogy and M. Schladt (1996, Comput. Vision Graphics Image Process. 63, 394–396) as well as L. Lateki (1993, Comput. Vision Graphics Image Process. 57, 261–262) deal with the topology on graphs. In this note, using a theorem given by P. Prea (1992, Discrete Math.103, 189–197), we will give new, simpler and shorter proofs of these results, we will generalize some of them.