2-Walk-Regular Dihedrants from Group-Divisible Designs
Keywords:
2-walk-regular graphs, Distance-regular graphs, Association schemes, Group divisible designs with the dual property, Relative cyclic difference sets, 2-arc-transitive dihedrants
Abstract
In this note, we construct bipartite $2$-walk-regular graphs with exactly 6 distinct eigenvalues as the point-block incidence graphs of group divisible designs with the dual property. For many of them, we show that they are 2-arc-transitive dihedrants. We note that some of these graphs are not described in Du et al. (2008), in which they classified the connected 2-arc transitive dihedrants.