Question Type 2: Finding minimum spanning trees by applying Kruskal's algorithm Exercises

Given the weighted undirected graph with vertices $A,B,C,D$ and edges with weights: $(A,B)=1, (A,C)=3, (A,D)=4, (B,C)=2, (C,D)=5$. Use Kruskal's algorithm to find the minimum spanning tree (MST). List the edges in the MST and its total weight.

The graph has vertices $A,B,C,D,E$ and weighted edges: $(A,B)=2, (A,C)=4, (B,D)=3, (C,D)=5, (B,C)=1, (D,E)=6, (C,E)=7$. Apply Kruskal's algorithm to determine the MST and compute its total weight.

Consider the graph with vertices $1,2,3,4,5$ and weights: $(1,2)=10, (1,3)=8, (1,4)=5, (2,3)=7, (2,5)=6, (3,4)=9, (4,5)=2, (3,5)=3$. Use Kruskal's algorithm to find the minimum spanning tree and its total weight.

Consider the graph on vertices $1,2,3,4,5,6$ with edges and weights: $(1,2)=3, (1,3)=1, (2,3)=7, (2,4)=5, (3,5)=4, (4,5)=2, (4,6)=6, (5,6)=8$. Use Kruskal's algorithm to find its MST and state its total weight.

The graph has 6 vertices labeled $1$–$6$ and weighted edges: $(1,2)=5, (1,3)=2, (1,4)=4, (2,3)=3, (2,5)=6, (3,4)=7, (3,6)=8, (4,5)=1, (5,6)=9$. Apply Kruskal's algorithm to find the MST and its sum of weights.

A weighted graph has vertices $A,B,C,D,E$ and edges: $(A,B)=3, (A,C)=2, (A,D)=4, (B,C)=1, (B,E)=5, (C,D)=6, (C,E)=7, (D,E)=8$. Apply Kruskal's algorithm to determine the MST and its weight.

A graph on vertices $A,B,C,D,E,F,G$ has edges and weights: $(A,B)=2, (A,C)=4, (B,C)=1, (B,D)=5, (C,E)=3, (D,E)=6, (D,F)=7, (E,G)=8, (F,G)=9$. Find the MST using Kruskal's algorithm and state its total weight.

A graph on vertices $A,B,C,D,E,F$ has edges and weights: $(A,B)=2, (A,C)=5, (B,C)=1, (B,D)=4, (C,E)=3, (D,E)=6, (D,F)=7, (E,F)=8$. Use Kruskal's algorithm to derive the MST and its overall weight.

A complete graph has vertices $A,B,C,D,E$ and edge weights: $(A,B)=2, (A,C)=9, (A,D)=3, (A,E)=6, (B,C)=1, (B,D)=7, (B,E)=8, (C,D)=4, (C,E)=5, (D,E)=10$. Find the MST via Kruskal's algorithm and its total weight.

Given vertices $P,Q,R,S,T,U,V$ and edges: $(P,Q)=3, (P,R)=2, (Q,R)=1, (Q,S)=4, (R,T)=5, (S,T)=6, (S,U)=7, (T,V)=8, (U,V)=9$. Use Kruskal's algorithm to determine the MST and compute its total weight.

Vertices $1,2,3,4,5,6,7$ are connected by edges with weights: $(1,2)=4, (1,3)=2, (2,3)=1, (2,4)=7, (3,5)=5, (4,5)=3, (4,6)=6, (5,7)=8, (6,7)=9$. Find the MST using Kruskal's algorithm and state its total weight.