Classification of two-distance-transitive Cayley graphs of the semi-dihedral groups

2026/07/22 by Wei Jin, Cai Xia Li, Ping Shan Li
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Abstract

The class of 2-distance-transitive graphs naturally generalizes distance-transitive graphs and plays a central role in algebraic graph theory. Classifying such graphs for a prescribed underlying group is a key open problem. A vertex-transitive graph Γ is said to be 2-distance-transitive if, for each i∈ \1,2\, any two pairs of vertices with identical distance i in Γ can be mapped to each other via some automorphism of the graph. In this paper, we present a complete classification of all 2-distance-transitive Cayley graphs of the semi-dihedral groups.

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