2026/07/21 by Wei Jin, Yu Xiang Jin, Cai Xia Li +1
#math.CO
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 \citeJZ-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 \(\Kn\), the complete bipartite graph \(\Kn/2,n/2\), the graph \(\Kn/2,n/2-(n)/(2)\K2\) (with \(n/2\) odd), the cycle \(\Cn\), the directed cycle \( \Cn\), a normal circulant digraph of prime valency, the lexicographic product \( \Cm[\Kb]\), or the tensor product \( \Cm× \Kb\) with \(gcd(m,b)=1\).