It is clear that the term Moore graph was coined by Hoffman and Singleton in their paper On Moore graphs with diameters $2$ and $3$, where they write
E. F. Moore has posed the problem of describing graphs for which equality holds in (2). We call such graphs "Moore graphs of type $(d,k)$".
My question is: does anyone know where Moore posed this problem?
Moore posed this problem to Hoffman at a conference, so it is not in print. Hoffman makes the following remark (from "Selected Papers of Alan Hoffman with Commentary", pp. 367):
After I discussed the preceding paper at an IBM summer workshop, E.F. Moore raised the graph theory problem described in the paper, and my GE colleague Bob Singleton and I pondered it. Moore told me the problem because he thought the eigenvalue methods I was using might find another "Moore graph" of diameter 2 besides the pentagon and the Petersen graph. Indeed, we found the Hoffman-Singleton graph with 50 nodes (and showed it was unique) and that any other Moore graph of diameter 2 had to have 3,250 nodes (and to this day, no one knows if such a graph exists). Moore declined joint authorship, so we thanked him by giving his name to the class of graphs. When it was later proved by Damerell, and also by Bannai and Ito, that there were no other Moore graphs other than the trivial odd cycles, I felt a twinge of guilt in giving Moore's name to such a small set. But I was wrong: Moore graphs, Moore geometries, etc. continue to be discussed in the profession.
