
COMMENTS

Comment from Allan C. Wechsler, Nov 22 2015: a(8) <= 65 by the Moore bound. Since 8 is not in {2,3,7,57}, we know a(8) <= 64. I don't know if we have any better upper bounds. This seems like a decent undergraduate research project. Pushing up the lower bound also.


REFERENCES

Hoffman, Alan J.; Singleton, Robert R., Moore graphs with diameter 2 and 3, IBM Journal of Research and Development 5 (1960), 497504.
Loz, Eyal; Siran Jozef, New record graphs in the degreediameter problem, Australasian Journal of Combinatorics 41 (1968), 6380.
McKay, Brendan D.; Miller, Mirka; Siran, Jozef, A note on large graphs of diameter two and given maximum degree, Journal of Combinatorial Theory Series B 74 (1968): 110118.
PinedaVillavicencio, Guillermo; Gómez, José; Miller, Mirka; PérezRosésd, Hebert, New Largest Graphs of Diameter 6, Electronic Notes in Discrete Mathematics 24 (2006), 153160.


LINKS

Table of n, a(n) for n=1..7.
F. Comellas, (Degree,Diameter) Problem for Graphs
J. Dinneen, Michael; Hafner, Paul R., New Results for the Degree/Diameter Problem, Networks 24 (1995), 359367, arXiv:math/9504214.
Mirka Miller, Jozef Sirán, Moore Graphs and Beyond: A survey of the Degree/Diameter Problem, Electronic Journal of Combinatorics, Dynamic Survey DS14.
Wikipedia, Table of the largest known graphs of a given diameter and maximal degree
Wikipedia, HoffmanSingleton Graph
