AI 中文总结
本文聚焦半二面体群的二距离传递凯莱图分类问题，通过特定方法，给出了该类图的完整分类，为代数图论相关研究提供了重要成果。
AI 中文摘要
二距离传递图的类别自然推广了距离传递图，在代数图论中起核心作用。对给定基础群的此类图进行分类是关键的开放问题。若顶点传递图Γ中，对于每个i∈{1,2}，Γ中任意两对距离为i的顶点可通过图自同构相互映射，则称Γ是二距离传递的。本文给出了半二面体群所有二距离传递凯莱图的完整分类。
英文摘要
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 $i\in \{1,2\}$, 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.
