Moore graph with parameters (3250,57,0,1) does not exist

A. A. Makhnev

If a regular graph of degree $k$ and diameter $d$ has $v$ vertices then $$v\le 1+k+k(k-1)+\cdots +k(k-1{)}^{d-1}.$$ Graphs with $v=1+k+k(k-1)+\cdots +k(k-1{)}^{d-1}$ are called Moore graph…