Inspired by the combinatorial constructions in earlier work of authors that generalized classical Alexander polynomial to a large class spatial graphs with balanced weight on edges, we show value evaluated at [Formula: see text] gives weighted number spanning trees graph.

The network reconfiguration problem seeks to find a rooted tree T such that the energy of (unique) feasible electrical flow over is minimized. requirement on support motivated by operational constraints in electricity distribution networks. bulk existing results convex optimization vertices polytopes and structure flows do not easily give guarantees for this problem, while many heuristic method...