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How do you count spanning trees in a graph?
Cayleys formula states that for a complete graph on nvertices, the number of spanning trees is n^(n-2). For a complete bipartite graph we can use the formula p^q-1 q^p-1. for the number of spanning trees. A generalization of this for any graph is Kirchhoff's theorem or Kirchhoff's matrix tree theorem. This theorem looks at the Laplacian matrix of a graph. ( you may need to look up what that is with some examples). For graphs with a small number of edges and vertices, you can find all the spanning trees and this is often quicker. There are also algorithms such as depth-first and breadth-first for finding spanning trees.
How many rows of trees if there are 100 trees and there are 5 trees in each row how many rows of trees are there?
20 trees
How many are 25 million trees?
25 million trees are 25 million trees.
How many ways can a gardener plant 30 trees in rows so that each row contains the sames number of trees?
Six ways. 15 rows of 2 trees 6 rows of 5 trees 3 rows of 10 trees and 2 rows of 15 trees 5 rows of 6 trees 10 rows of 3 trees * * * * * How about 1 row of 30 trees and 30 rows of 1 tree each?
How many trees were damaged if a storm damaged 12 percent of 6250 trees?
750 trees were damaged.
