AI 中文总结
研究局部拟本原循环有向图的分类，通过扩展局部本原循环图分类，确定其同构类型包括完全图、完全二部图等多种图，给出了连通局部拟本原循环有向图的具体分类结果。
AI 中文摘要
循环有向图是有限循环群上的凯莱有向图，是代数图论中的基本对象类。扩展局部本原循环图的分类，我们完全确定了所有局部拟本原循环有向图。主要定理表明，连通的局部拟本原循环有向图同构于以下之一：完全图\(\K_n\)、完全二部图\(\K_{n/2,n/2}\)、图\(\K_{n/2,n/2}-\frac{n}{2}\K_2\)（\(n/2\)为奇数）、圈\(\C_n\)、有向圈\(\vec \C_n\)、素价正规循环有向图、字典序积\(\vec \C_m[\overline{\K_b}]\)或张量积\(\vec \C_m\times \K_b\)（\(\gcd(m,b)=1\)）。
英文摘要
Circulant digraphs are Cayley digraphs over finite cyclic groups and constitute a fundamental class of objects in algebraic graph theory. Extending the classification of locally-primitive circulant graphs \cite{JZ-2026}, we completely determine all locally-quasiprimitive circulant digraphs. Our main theorem shows that a connected locally-quasiprimitive circulant digraph is isomorphic to one of the following: the complete graph \(\K_n\), the complete bipartite graph \(\K_{n/2,n/2}\), the graph \(\K_{n/2,n/2}-\frac{n}{2}\K_2\) (with \(n/2\) odd), the cycle \(\C_n\), the directed cycle \(\vec \C_n\), a normal circulant digraph of prime valency, the lexicographic product \(\vec \C_m[\overline{\K_b}]\), or the tensor product \(\vec \C_m\times \K_b\) with \(\gcd(m,b)=1\).
