关于（K，d）－算术图的两个猜想

On the Conjectures of (K,d) Arithmetic Graphs

文献［１］中猜想：（１）若Ｃ４ｔ＋１是（Ｋ，ｄ）－算术图，则有非负整数ｒ，使得Ｋ＝２ｄｔ＋２ｒ；（２）如果Ｃ４ｔ＋３是（Ｋ，ｄ）－算术图，则有非负整数ｒ，使得Ｋ＝（２ｔ＋１）ｄ＋２ｒ。

he following conjectures have been presented in : (1) If C 4t+1 is (K,d) arithmetic, then K=2dt+2r for some integer r≥0 ; (2) If C 4t+3 is (K,d) arithmetic, then K=(2t+1)d+2r for some integer r≥0 . In this paper, the above conjectures prove true.