2-Walk-Regular Dihedrants from Group-Divisible Designs

Zhi Qiao, Shao Fei Du, Jack H Koolen

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. 


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

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