Monotonicity of maximum algebraic connectivity with girth

For integers $d$, $n$, and $g$, let $f(g;d,n)$ be the maximum possible algebraic connectivity among graphs of degree $d$, order $n$, and girth $g$.

Algebraic-connectivity monotonicity conjecture. The function $f(g;d,n)$ is increasing as a function of $g$.

This is presented as a stronger conjecture motivated by the same computational data on cubic and quartic graphs. It remains an open problem.