Extremal non-bipartite regular graphs of girth 4 (Q5903455)

Let \(f(r)\) denote the smallest number of points in a non-bipartite \(r\)-regular graph of girth 4. \textit{D. Bauer} [J. Comb. Theory, Ser. B, 37, 64-69 (1984; Zbl 0528.05038)] asked whether \(f(25)=66\). We prove that this is so and, more generally, we prove that \(f(4n+1)=10n+6\) \((n\geq 3)\).