# A Note on Large Graphs of Diameter Two and Given Maximum Degree,

@article{McKay1998ANO, title={A Note on Large Graphs of Diameter Two and Given Maximum Degree,}, author={Brendan D. McKay and Mirka Miller and Jozef Sir{\'a}n}, journal={J. Comb. Theory, Ser. B}, year={1998}, volume={74}, pages={110-118} }

Letvt(d,2) be the largest order of a vertex-transitive graph of degreedand diameter 2. It is known thatvt(d,2)=d2+1 ford=1,2,3, and 7; for the remaining values ofdwe havevt(d,2)?d2?1. The only knowngenerallower bound onvt(d,2), valid forall d, seems to bevt(d,2)??(d+2)/2? ?(d+2)/2?. Using voltage graphs, we construct a family of vertex-transitive non-Cayley graphs which shows thatvt(d,2)?(8/9)(d+12)2for alldof the formd=(3q?1)/2, whereqis a prime power congruent with 1 (mod 4). The construction…

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