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