An explicit characterization of arc-transitive circulants
Cai Heng Li, Binzhou Xia, Sanming Zhou
TL;DR
This paper provides an explicit characterization of arc-transitive circulants and their automorphism groups, proving that all such circulants are CI-digraphs, thereby advancing understanding of their structure and symmetry properties.
Contribution
It offers a new explicit characterization of arc-transitive circulants and their automorphism groups, and proves they are all CI-digraphs, clarifying their structural properties.
Findings
Explicit characterization of arc-transitive circulants
Proof that all arc-transitive circulants are CI-digraphs
Enhanced understanding of automorphism groups of circulants
Abstract
A reductive characterization of arc-transitive circulants was given independently by Kovacs in 2004 and the first author in 2005. In this paper, we give an explicit characterization of arc-transitive circulants and their automorphism groups. Based on this, we give a proof of the fact that arc-transitive circulants are all CI-digraphs.
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Taxonomy
TopicsFinite Group Theory Research · Algebraic structures and combinatorial models · Advanced Topics in Algebra