**Combinatorial and Discrete Geometry: Sheet E**

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

1. Given the graph G below:

a. Write down the number of edges, vertices, and degree sequence of G

b. For each vertex v of the graph G draw the graph G - v and write down the degree sequence of G - v. Which of the graphs G - v are connected and if G - v is not connected how many components does G - v have?

c. For each edge e of the graph draw the graph G - e and write down the degree sequence of G - e. Which of the graphs G - e are connected and if G - e is not connected how many components does G - e have?

d. Can you see any patterns involving the degree sequence of G, and those you get for G - v or G - e?