**Sheet M
**

Prepared by:

Joseph Malkevitch

Department of Mathematics

York College (CUNY)

Jamaica, New York 11451

1. For the graph H below, find the subgraphs induced by the sets of vertices given:

a. { a, e } e. {a, e, f, h }

b. { e, b, g, h } f. {b, h, i, g }

c. { b, d, h, i } g. { b, d, e, f, h }

d. ( b, d, h, j } h. { b, f, h, i, g }

2. Is there any set of vertices in the graph above which will induce the subgraph shown in the diagram below?

3. Find the chromatic number and independence number for the graph in Problem 1.

4. List the cut vertices and the cut edges for the graph in Problem 1.

5. (a) What is the minimum number of edges that must be deleted from the graph H in Problem 1 to obtain a tree.

(b) Draw:

i. H\edge [b,h]

ii. H\edge [b,f]

iii. H | edge [e. f]

iv. H | edge [e,b]