In this paper, the integral Cayley graphs over the nonabelian group V_8n = 〈a, b | a²ⁿ = b⁴ = 1, ba = a⁻¹b⁻¹, b⁻¹a = a⁻¹b〉 are studied, where n is an odd integer. Character tables of V_8n are used to provide a necessary and sufficient condition for the integrality of such Cayley graphs. This is then translated into a simple necessary and sufficient condition for integrality in terms of the associated Boolean algebra of 〈a²〉. This leads to a construction of several infinite families of connected integral Cayley graphs over V_8n. Finally, a necessary and sufficient condition for the integrality of Cayley graphs over V_8p for a prime p is given.

在本文中，非阿贝尔群上的积分凯莱图V _{8 n}  = < a , b  | 研究了a ^{2 n}  =  b ⁴  = 1, ba  =  a ⁻¹ b ⁻¹ , b ⁻¹ a  =  a ⁻¹ b 〉，其中n为奇数。V _{8 n}的字符表用于为此类 Cayley 图的完整性提供充分必要条件。然后根据 < a ² > 的相关布尔代数将其转化为完整性的简单充分必要条件。这导致在V _{8 n}上构造多个连接的积分 Cayley 图的无限族。最后，给出了素数p在V _{8 p}上凯莱图的完整性的充分必要条件。