2-walk-regular dihedrants from group-divisible designs

TL;DR

This paper constructs specific bipartite 2-walk-regular graphs from group-divisible designs, many of which are 2-arc-transitive dihedrants, expanding the understanding of such graph structures.

Contribution

It introduces new bipartite 2-walk-regular graphs from group-divisible designs with the dual property, many being 2-arc-transitive dihedrants, not previously classified.

Findings

Constructed bipartite 2-walk-regular graphs with 6 eigenvalues

Many graphs are 2-arc-transitive dihedrants

Some graphs are new and not in existing classifications

Abstract

In this note, we construct bipartite 2-walk-regular graphs with exactly 6 distinct eigenvalues as 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 many of these graphs are not described in Du et al. [7, Theorem1.2], in which they classify the connected 2-arc transitive dihedrants.