Strongly regular graphs and group divisible designs

2-Walk-Regular Dihedrants from Group-Divisible Designs

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.

Walk-regular divisible design graphs

A divisible design graph (DDG for short) is a graph whose adjacency matrix is the incidence matrix of a divisible design. DDGs were introduced by Kharaghani, Meulenberg and the second author as a generalization of (v, k, λ)-graphs. It turns out that most (but not all) of the known examples of DDGs are walk-regular. In this paper we present an easy criterion for this to happen. In several cases ...

Construction of Group Divisible Designs

Strongly regular graphs and the Higman-Sims group

We introduce some well known results about permutation groups, strongly regular graphs, design theory and finite geometry. Our goal is the construction of the Higman-Sims group as an index 2 subgroup of the automorphism group of a (100, 22, 0, 6)-srg. To achieve this we introduce some tools from design theory. Some of the arguments here are slightly more general than those given in lectures. Al...

Strongly regular graphs

Strongly regular graphs form an important class of graphs which lie somewhere between the highly structured and the apparently random. This chapter gives an introduction to these graphs with pointers to more detailed surveys of particular topics.