Graphs derived from perfect difference sets

Erskine, Grahame; Fratrič, Peter and Širáň, Jozef (2021). Graphs derived from perfect difference sets. Australasian Journal of Combinatorics, 80(1) pp. 48–56.



We study a family of graphs with diameter two and asymptotically optimal order for their maximum degree, obtained from perfect difference sets. We show that for all known examples of perfect difference sets, the graph we obtain is isomorphic to one of the Brown graphs, a well-known family of graphs in the degree-diameter problem.

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