504
Graphs and Trees
41.
3
1
2
4
42.
1
3
4
2
For Exercises 43–46, draw the graph represented by the adjacency matrix.
43.
£
0 2 0
2 0 2
0 2 0
§
45.
E
0 1 1 1 0
1 0 0 0 1
1 0 0 0 1
1 0 0 0 1
0 1 1 1 0
U
44.
F
0 1 0 0 0 0
1 0 1 0 0 0
0 1 1 1 0 0
0 0 1 0 0 0
0 0 0 0 0 2
0 0 0 0 2 0
V
46.
E
0 1 0 0 1
1 0 1 0 0
0 1 0 1 0
0 0 1 0 1
1 0 0 1 0
U
47. The adjacency matrix for an undirected graph is given in lower triangular form by
2
1
0
0
0
1
1
1
2
0
Draw the graph.
48. The adjacency matrix for a directed graph is given by
E
0 1 1 0 0
0 0 0 0 0
0 0 1 1 0
0 0 1 0 2
1 0 0 0 0
U
Draw the graph.
49. Describe the graph whose adjacency matrix is I n , the n × n identity matrix.
50. Describe the graph whose adjacency matrix is 0 n , the n × n matrix of all 0’s.
51. Describe the adjacency matrix for K n , the simple, complete graph with n nodes.