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.
20 trees
25 million trees are 25 million 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?
750 trees were damaged.
Gabon's most useful resouce is the lumber from the rain forest trees.
there are many useful trees such as dalbergia sisoo, tectona grandis,poplar, eucalyptus and plants such as acacia augustifolia.
9x9=81. Proving that one of the factor trees for 81 is 9xp.
tanning etc.
Sloths mainly hang in trees and eat bugs. Yum. Useful? Phft!
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.
What I think about the trees is that, they shed their over-grown and no-more useful leaves in the season of Autumn. This is how I think that trees get rid of their waste.
Monkeys are useful to trees, in many cases, because they eat the trees' fruits, but don't digest the seeds. Then, they disperse the seeds, (via their dung) far from the parent tree.
Monkeys are useful to trees, in many cases, because they eat the trees' fruits, but don't digest the seeds. Then, they disperse the seeds, (via their dung) far from the parent tree.
Wild animals are useful to us because they provide food. Also, they are useful in the life cycle with trees in producing oxygen for us to breathe.
Branching trees are useful because they provide a hierarchical structure for organizing and searching data efficiently. They help in facilitating quick retrieval and insertion of data, such as in algorithms like binary search trees. Additionally, branching trees enable a clear visualization of relationships between different data points or categories.
In addition to eating them: Many species of mushrooms, for example, pair with certain species of trees in symbiotic relationships that allow both to thrive. The trees, thanks to the mushrooms, are useful to us in many ways.