In a weighted undirected graph of n nodes, what is the minimum cost of visiting any distinct k nodes? -

here different k nodes visitees, visited visitors. challenge that, number of visitors, visitors, k distinct visitees, , visiting path (from visitor visitees) need decided. rule visitee can not vistor. here several examples:

if k=1, find edge minimum weight in graph, (u,v), either u visitor (then v visitee) or v visitor (then u visitee). minimum cost minimum weight.

if k=2, find 2 edges minimum weights in graph, (u,v) , (u',v'). if u,v, u',v' 4 different nodes, node in 1 of 2 edges can visitor , other node visitee. if 1 node both edges same, v=u', can u visitor , v, v' visitees, or v' visitor , v, u visitees, both optimal solution.

if k=3, however, finding 3 minimum weighted edges not give optimal solution. here example. say, edges (u,v), (v,u'), , (v,v') 3 edges. can u visits both v , u'. however, since v being visited, can not visitor visit v'. v' can not visitor visits v either, since v can visited once. in case, have find fourth-minimum edge.

the maximum value of k n-1, in case, should find 1 visitor visit other n-1 visitees using least cost. here unlike tsp, possible node visited multiple times, since our graph not complete graph. map problem tsp: want visit k cities (the visitees) out of n cities using least cost - achieve that, don't mind have many possible salesmen (the visitors), , don't mind city start at, care k cities being visited, , possible city visited multiple times; besides, n cities not form complete graph.

thanks input.