Let $G=(V,E)$ be a undirected simple graph, and $\Omega(G)$ denote the set of spanning trees of G. Does the next funcion $$l(G) = \min_{T \in \Omega(G)}\quad \sum_{uv \in E} \mbox{dist}_T(u,v)$$ have a specific name? Or has it been studied before?.

The problem is NP-hard, but I'm particularly interested in lower bounds of $l(G)$. Both for general graphs and for specific topologies.