Abstract
In this last chapter of Part I, the focus is on local relationships between elements of a line graph. Among these are discrete analogues of the geometric concepts of diameter, radius, and center. Some of the results involve connections for these quantities between graphs and their line graphs, and what happens to their values in iterated line graphs. The center of a graph is also defined in a natural way, and some intriguing results on the center of a line graph are described. The other topic is in response to a question about partially ordered sets: Which line graphs can their edges oriented so that the result is a transitive ordering? The answer can be given in terms of forbidden subgraphs.
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