Chapter 14.4, Problem 34E

Town Water Distribution A town council is planning to provide town water to an area that previously relied on private wells. Water will be fed into the area at the point represented by the vertex labeled A in the graph on the next page. Water must be piped to each of five main distribution points, represented by the vertices labeled B through F in the graph. Town engineers have estimated the cost of laying the pipes to carry the water between each pair of points in millions of dollars, as indicated in the graph. They must now select which pipes should be laid, so that there is exactly one route for the water to be pumped from A to any one of the five distribution points (possibly via another distribution point), and they want to achieve this at minimum cost. Use Kruskal’s algorithm to decide which pipes should be laid. Find the total cost of laying the pipes.