Question

mst weight:

Explanation:

Step1: Recall MST concept

A minimum - spanning tree (MST) of a connected, edge - weighted undirected graph is a subset of the edges that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

Step2: Apply Prim's or Kruskal's algorithm (conceptually)

For a graph with all edge weights equal to 1, we can simply count the number of edges in the MST. For a connected graph with $n$ vertices, the number of edges in an MST is $n - 1$. Here, the number of vertices $n=7$.

Step3: Calculate the weight of the MST

Since each edge has a weight of 1 and the number of edges in the MST is $n - 1=7 - 1 = 6$, and the weight of each edge is 1, the total weight of the MST is the sum of the weights of its edges. So the weight of the MST is $6\times1=6$.

Answer:

6