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arXiv · 2607.19668

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

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 $\Gamma$ is said to be $2$-distance-transitive if, for each $i\in \{1,2\}$, any two pairs of vertices with identical distance $i$ in $\Gamma$ 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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Wei Jin, Cai Xia Li, Ping Shan Li. 2026-07-22. Classification of two-distance-transitive Cayley graphs of the semi-dihedral groups. https://arxiv.org/abs/2607.19668

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