algorithms – A graph theory problem that bothers me

I wonder if there is a polynomial time algorithm for this problem.

If so, what should the algorithm do? Why is it right? Has there been any discussion in the academic circle?

$text{Problem:}$

Given a complete graph with n vertices,The edge weight between vertex $i$ and vertex $j$ is $b[i]times b[j]$

Under the condition that the degree of point i on spanning tree is DEG [i],let the sum of all edge weights on spanning tree is maximized.

$text{thx>_<}.$