On 2-distance-transitive circulant digraphs
Abstract
Circulant digraphs form a prominent class of Cayley digraphs defined on finite cyclic groups. Building on the existing classification of $2$-arc-transitive circulant graphs, this paper presents a complete classification of $2$-distance-transitive circulant digraphs. Our main theorem establishes that every connected $2$-distance-transitive circulant digraph is isomorphic to one of the following: the undirected cycle Cn, the complete bipartite graph Kn/2,n/2, the complete multipartite graph Km[b] with m≥ 3,b≥ 2, the graph Kn/2,n/2−n/2K2 for odd n/2, prime-order Paley graphs, the directed cycle overrightarrowCn, the oriented graph G(pm,r) satisfying Condition~\ref{p-power-normal-2dt-cond}, the oriented graph Cr(b,1) with r≥ 3,b≥ 2 and rb=n, the lexicographic product oriented graph G(pm,r)[K̅d] where G(pm,r) obeys Condition~\ref{p-power-normal-2dt-cond}.
Related
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- Automorphism groups of endomorphism monoids of $0$-unit $3$-valent circulant digraphs
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- Hamiltonicity and cycle factors in k-quasi-transitive digraphs of large diameter
- The Path Partition Conjecture and 3-(quasi-)Transitive Digraphs
BibTeX
@misc{jin20262distancetransitive,
title = {{On 2-distance-transitive circulant digraphs}},
author = {Wei Jin and Cai Xia Li and Ping Shan Li and Xiao Lin Sun and Jue Wu and Fan Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19734},
eprint = {2609.19734},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19734},
}
RIS
TY - UNPB
TI - On 2-distance-transitive circulant digraphs
AU - Wei Jin
AU - Cai Xia Li
AU - Ping Shan Li
AU - Xiao Lin Sun
AU - Jue Wu
AU - Fan Yang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19734
UR - https://arxiv.org/abs/2609.19734
AB - Circulant digraphs form a prominent class of Cayley digraphs defined on finite cyclic groups. Building on the existing classification of $2$-arc-transitive circulant graphs, this paper presents a complete classification of $2$-distance-transitive circulant digraphs. Our main theorem establishes that every connected $2$-distance-transitive circulant digraph is isomorphic to one of the following: the undirected cycle C_n, the complete bipartite graph K_n/2,n/2, the complete multipartite graph K_m[b] with m≥ 3,b≥ 2, the graph K_n/2,n/2−n/2K_2 for odd n/2, prime-order Paley graphs, the directed cycle overrightarrowC_n, the oriented graph G(p^m,r) satisfying Condition~\ref{p-power-normal-2dt-cond}, the oriented graph C_r(b,1) with r≥ 3,b≥ 2 and rb=n, the lexicographic product oriented graph G(p^m,r)[K̅_d] where G(p^m,r) obeys Condition~\ref{p-power-normal-2dt-cond}.
ER -