In this paper are investigated abc—cubic graphs. The following theorems are obtained. Theorem 1 abe—cubic graphs without triangles exist iff triples (a

b

c) are the followings (1

1

1)

(1

1

2)

(1

1

3)

(1

2

2) (2

2

2). Theorem 2 Figure 12-1

Figure 13

Figure 14

Figure 15

and Figure 16 are the minimum graphs without triangles of 111—cubic

112—cubic

113—cubic

122—cubic and 222—cubic

respectively. Theorem 3 abc—cubic graphs exist iff triples (a

b

c) are the followings;:(1

1

1)

(1

1

2)

(1

1

3)

(1

1

4)

(1

1

5)

(1

2

2)

(1

2

3)

(1

2

4)

(1

3

3)

(2

2

2)

(2

2

3). Theorem 4 Figures from 23 to 33 are the minimum graphs of 111—cubic

112—cubic

113—cubic

114—cubic

115—cubic

122—cubic

123—cubic

124—cubic

133—cubic

222—cubic and 223—cubic