Regular-graph reformulation of Boesch's maximum-girth conjecture

Let a uniformly most reliable graph (UMRG) be a graph with the highest all-terminal reliability among graphs having the same order and size, for every edge-failure probability. For a graph, the girth $g$ is the length of its shortest cycle, and a $k$-regular graph has every vertex of degree $k$.

Regular Boesch conjecture. If an $(n,kn/2)$ UMRG exists and has girth $g$, then it has maximum girth among all $k$-regular $(n,kn/2)$-graphs and, among the $k$-regular $(n,kn/2)$-graphs with girth $g$, it has the minimum number of $g$-cycles.

This is presented as a reformulation of Boesch's maximum-girth conjecture. The supplied text does not give a separate resolution of this reformulation; the broader maximum-girth claim is nevertheless refuted by the reported 4-regular $(9,18)$ UMRG of girth $3$.