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- Title
FINITE TWO-DISTANCE-TRANSITIVE DIHEDRANTS.
- Authors
JIN, WEI; TAN, LI
- Abstract
A noncomplete graph is $2$ -distance-transitive if, for $i \in \{1,2\}$ and for any two vertex pairs $(u_1,v_1)$ and $(u_2,v_2)$ with the same distance i in the graph, there exists an element of the graph automorphism group that maps $(u_1,v_1)$ to $(u_2,v_2)$. This paper determines the family of $2$ -distance-transitive Cayley graphs over dihedral groups, and it is shown that if the girth of such a graph is not $4$ , then either it is a known $2$ -arc-transitive graph or it is isomorphic to one of the following two graphs: $ {\mathrm {K}}_{x[y]}$ , where $x\geq 3,y\geq 2$ , and $G(2,p,({p-1})/{4})$ , where p is a prime and $p \equiv 1 \ (\operatorname {mod}\, 8)$. Then, as an application of the above result, a complete classification is achieved of the family of $2$ -geodesic-transitive Cayley graphs for dihedral groups.
- Subjects
CAYLEY graphs; AUTOMORPHISM groups; MULTIPLY transitive groups; FINITE, The
- Publication
Journal of the Australian Mathematical Society, 2022, Vol 113, Issue 3, p386
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788721000409