Chapter 12.5, Problem 7E

(a)

To determine

Change the depth-first search algorithm so that it can count the number of connected components of a graph.

(b)

To determine

To prove: The number of components also, give the labels that the search assign to the vertices.

If the table shows the adjacencies in a graph with vertices $v_1,v_2,\mathrm{......}{v}_{13}$ without drawing the graph apply depth-first search and use the method discovered in part (a).

	1	2	3	4	5	6	7	8	9	10	11	12	13
1	0	1	0	0	0	1	0	0	0	0	1	0	0
2	1	0	0	0	0	0	0	0	0	0	1	0	0
3	0	0	0	0	0	0	0	1	0	0	0	0	1
4	0	0	0	0	1	0	1	0	0	0	0	1	0
5	0	0	0	1	0	0	0	0	0	1	0	0	0
6	1	0	0	0	0	0	0	0	0	0	1	0	0
7	0	0	0	1	0	0	0	0	1	1	0	0	0
8	0	0	1	0	0	0	0	0	0	0	0	0	1
9	0	0	0	0	0	0	1	0	0	0	0	1	0
10	0	0	0	0	1	0	1	0	0	0	0	0	0
11	1	1	0	0	0	1	0	0	0	0	0	0	0
12	0	0	0	1	0	0	0	0	1	0	0	0	0
13	0	0	1	0	0	0	0	1	0	0	0	0	0