We prove two results for directed strongly regular graphs that have an eigenvalue of multiplicity less than k, the common out-degree of each vertex. The first bounds the size of an independent set, and the second determines an eigenvalue of the subgraph on the out-neighborhood of a vertex. Both lead to new nonexistence results for parameter sets.

We prove a generalization of a theorem of Ganter concerning the embedding of partial Steiner systems into Steiner systems. As an application we discuss a further version of the problem of Rosenfeld on embedding graphs into strongly regular graphs.

We show that ω-categorical rings with NIP are nilpotent-by-finite. We prove that an ω-categorical group with NIP and fsg is nilpotent-by-finite. We also notice that an ω-categorical group with at least one strongly regular type is abelian. Moreover, we get that each ω-categorical, characteristically simple p-group with NIP has an infinite, definable abelian subgroup. Assuming additionally the e...

Spreads of finite symplectic, orthogonal and unitary vector spaces are used to construct new strongly regular graphs having the same parameters as the perpendicularity graphs of the underlying vector spaces. Some of the graphs are. related to partial geometries, while others produce interesting symmetric designs.

Color segmentation is crucial in robotic applications, such as RoboCup, where the relevant objects can be distinguished by their color. In these applications, real-time performance and robustness are primary concerns. We present a hybrid method for color segmentation based on seeded region growing (SRG) in which the initial seeds are provided by a conservative threshold color segmentation. The ...

In this paper we construct transitive t-designs from the linear groups L(2, q), q ≤ 23. Thereby we classify t-designs, t ≥ 2, admitting a transitive action of the linear groups L(2, q), q ≤ 23, up to 35 points and obtained numerous transitive designs, for 36 ≤ v ≤ 55. In many cases we proved the existence of t-designs with certain parameter sets. Among others we constructed t-designs with param...

A graph is called of type k if it is connected, regular, and has k distinct eigenvalues. For example graphs of type 2 are the complete graphs, while those of type 3 are the strongly regular graphs. We prove that for any positive integer n, every graph can be embedded in n cospectral, non-isomorphic graphs of type k for every k ≥ 3. Furthermore, in the case k ≥ 5 such a family of extensions can ...

Let Y = (G, @, I ) be a linearly ordered, commutative group and u@u = max(u, t’) for all u, IJEG. Extend 0, @ in the usual way on matrices over G. An m x n matrix A is said to have strongly linearly independent (SLI) columns, if for some b the system of equations A@x = b has a unique solution. If, moreover, m = n then A is said to be strongly regular (SR). This paper is a survey of results conc...

The Hankel matrix has various applications. In this paper we prove that Hankel matrix is strongly regular and apply to obtain the necessary and sufficient conditions to sum the Walsh–Fourier series of a function of bounded variation. 2013 Elsevier Inc. All rights reserved.

Combining results on quadrics in projective geometries with an algebraic interplay between finite fields and Galois rings, we construct the first known family of partial difference sets with negative Latin square type parameters in nonelementary abelian groups, the groups Z 4 × Z4`−4k 2 for all k when ` is odd and for all k < ` when ` is even. Similarly, we construct partial difference sets wit...