We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries their generalizations or elliptic semiplanes are constructed. Necessary existence conditions proved a table of feasible parameters at most 200 points is presented. Non-existence some proved.

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner 2-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency.

The statistical properties for bicoherence estimation are shown to be strongly connected to the properties of the powerand bispectral estimator used. Data tapering will reduce spectral leakage and frequency smoothing will reduce the variance. It is shown that correct normalization is essential to ensure unbiased results. The multitaper approach is shown to be superior to other non-parametric es...

where J is the all ones matrix and I is the identity. These matrix conditions are equivalent to the combinatorial conditions that the graph is both inand out-regular, and that the number of directed 2-paths from a vertex x to a vertex y is t if x = y, λ if x → y, and μ otherwise. Recently, these graphs were studied by Klin et al. [2], including some new constructions and a list of feasible para...

We consider a strongly regular graph, G, and associate a three dimensional Euclidean Jordan algebra, V, to the adjacency matrix A of G. Then, by considering convergent series of Hadamard powers of the idempotents of the unique complete system of orthogonal idempotents of V, we establish new feasibility conditions for the existence of strongly regular graphs.

A distributed algorithm is developed that can be used to compute the topology of a network, given that each site starts with information about sites it is adjacent to, the network is strongly connected, and communication channels are unidirectional. The program is derived using assertional reasoning.

I point out that an “infinite-dimensional, homogeneous, pregeometry” on a structure M is the same thing as a generically stable type p(x) such that (p(x), x = x) is strongly regular. I also discuss the case of quasi-minimal structures and groups.

In 1959 S.S. Shrikhande wrote a paper concerning L2 association schemes [11]. Out of this paper arose a strongly regular graph with parameters (16, 6, 2, 2) that was not isomorphic to L2(4). This graph turned out to be important in the study of strongly regular graphs as a whole. In this paper, we survey the various constructions and properties of this graph.