**Combinatorial and Discrete Geometry: Sheet L**

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Studies

York College (CUNY)

Jamaica, New York 11451

email: joeyc@cunyvm.cuny.edu

web page: http://www.york.cuny.edu/~malk

Definition:

A tree is a connected graph without cycles.

If t_{i} denotes the number of vertices of a tree with valence i, verify that the following equation holds for the valences of the vertices of a tree, where n denotes the vertex of max valence in the tree:

G:

H:

I:

J: