Given a connected graph with $|V| = 10$ and $|E| = 20$, with $3$ edges of weight $3$, $4$ edges of weight $4$ and the remaining of weight $9$. What is the lowest weight in the subgraph spanning tree of the given graph?
I'm thinking of using the Kruskal algorithm, but have no idea how to do so, since there are no given edges.
Without knowing the structure of the graph, it is not possible to definitively answer the question with the given information.
For example, if 3-weighted edges form a triangle ($K_3$), or 4-weighted edges form $K_3$ or $K_4$, those edges need to be deleted from the graph. But, if these edges don't belong to any clique, then the answer is easy: Since a tree with 10 vertices will have 9 edges, using 2 edges with a weight of 9 together with all 3 and 4 weighted edges will result in a spanning tree with a weight of 43.