Square of a Graph

1
Square of a Graph

• Let G be a graph. The square of G, denoted by

, is the graph with

• Example Square of P7 Square of C9

2

• Theorem 1

• Example

3
5
8
10
13
16
18
21
23
26
0
k 5, diam(G)5 rn(G)26
3

• Theorem 2

0
15
7
10
3
12

• Example

4
13
6
9
K 3, diam(G) 3 rn(G)16
1
16
4

• Theorem 3

• Example

10
0
7
3
12
13
4
6
1
9
k 2, diam(G)3 rn(G)13
5

• Theorem 4

• Example

1
4
9
21
14
12
24
17
0
3
7
15
6
10
18
23
20
k 4, diam(G)4 rn(G)24
6

• Theorem 5