ABSTRACT
Through any point not on a given line, there passes a unique line having no points in common with the given line. Euclid through any point not on a given line, there passes no line having no points in common with the given line. Two related invariants are the maximum number of nonadjacent points and lines. Two related invariants are the maximum number of nonadjacent points and lines. These four numbers associated with any graph satisfy several relations and also suggest the study of special points and lines which are critical for covering purposes. Criteria for the existence of such subgraphs are established in terms of covering properties of the graph. A point and a line are said to cover each other if they are incident. On the other hand, there are graphs which are equal to their line-core.
