The maximum-spanning-tree conjecture for Moore graphs

Let $G$ be a simple graph, and let $\tau(G)$ denote its number of spanning trees. A $k$-regular graph of girth $g$ with the minimum possible number of vertices is called a $(k,g)$-cage; when it attains the Moore bound, it is a Moore graph. Moore-graph spanning-tree conjecture. Moore graphs have the maximum number of spanning trees among all simple graphs with the same number of vertices and edges.

This conjecture extends the observed extremal behavior of complete graphs, complete bipartite graphs, and the Petersen graph, but the source gives no resolution.