It is clear that the term [*Moore graph*](https://en.wikipedia.org/wiki/Moore_graph) was coined by Hoffman and Singleton in their paper [On Moore graphs with diameters $2$ and $3$](https://doi.org/10.1147/rd.45.0497), 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?



Reference request: Moore graphs
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.
> 
> 
> 


