Edge Rotation and Edge Slide Distance Graphs

Let S be a set of graphs and d a distance function defined on S × S. The distance graph (S) of S is that graph whose vertex set is S, and in which two vertices G and H are adjacent if and only if d(G, H) = 1. In this paper, we define two types of distance between graphs and discuss properties of the corresponding distance graphs. We also investigate those graphs that are distance graphs.