1-tree
= 1-tree
= One-tree
{synonym}
For a designated root vertex in an undirected complete graph, a 1-tree consists of a <spanning tree> on all other vertices together with two distinct root-incident edges. It is connected and has exactly one cycle, which passes through the root. Its minimum weight is the cost of an independent <minimum spanning tree> plus the two cheapest root edges, computable in quadratic time on a dense graph by <Prim's algorithm>.