Non-derivable strongly regular graphs from quasi-symmetric designs

Strongly regular graphs with non-trivial automorphisms

Half-regular symmetric designs

This paper is of an investigation of symmetric 2 (v, k,'x) designs such that the point set and the block set can each be halved to give a tactical decomposition. We assume that there is a group of automorphisms of the design of order v /2 which has two orbits of points, each of length v /2. Only the identity fixes a point, and we say that such a group acts half-regularly on the design. The desi...

Quasi-Spectral Characterization of Strongly Distance-Regular Graphs

A graph Γ with diameter d is strongly distance-regular if Γ is distanceregular and its distance-d graph Γd is strongly regular. The known examples are all the connected strongly regular graphs (i.e. d = 2), all the antipodal distanceregular graphs, and some distance-regular graphs with diameter d = 3. The main result in this paper is a characterization of these graphs (among regular graphs with...

New Symmetric Designs from Regular Hadamard Matrices

For every positive integer m, we construct a symmetric (v, k, λ)-design with parameters v = h((2h−1) 2m−1) h−1 , k = h(2h − 1)2m−1, and λ = h(h − 1)(2h − 1)2m−2, where h = ±3 · 2 and |2h − 1| is a prime power. For m ≥ 2 and d ≥ 1, these parameter values were previously undecided. The tools used in the construction are balanced generalized weighing matrices and regular Hadamard matrices of order...

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.