In many real-life scenarios, a group of agents needs to agree on a common action, e.g., on a location for a public facility, while there is some consistency between their preferences, e.g., all preferences are derived from a common metric space. The facility location problem models such scenarios and it is a well-studied problem in social choice. We study mechanisms for facility location on unweighted undirected graphs, which are resistant to manipulations (strategy-proof, abstention-proof, and false-name-proof) by both individuals and coalitions and are efficient (Pareto optimal). We define a family of graphs, ZV-line graphs, and show a general facility location mechanism for these graphs which satisfies all these desired properties. Our result unifies the few works in the literature of false-name-proof facility location on discrete graphs including the preliminary (unpublished) works we are aware of.