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.

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.

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.

Let V be a real finite dimensional representation of a compact Lie group G. It is well-known that the algebra R[V ] of G-invariant polynomials on V is finitely generated, say by σ1, . . . , σp. Schwarz [38] proved that each G-invariant C-function f on V has the form f = F (σ1, . . . , σp) for a Cfunction F on R. We investigate this representation within the framework of Denjoy–Carleman classes....

The group PGL(2, q) has an embedding into PGL(3, q) such that it acts as the group fixing a nonsingular conic in PG(2, q). This action affords a coherent configuration R(q) on the set L(q) of non-tangent lines of the conic. We show that the relations can be described by using the cross-ratio. Our results imply that the restrictions R+(q) and R−(q) of R(q) to the set L+(q) of secant (hyperbolic)...

In this paper, we consider a generalization of Ebenbauer’s differential equation for non-symmetric matrix diagonalization to a flow on arbitrary complex semisimple Lie algebras. The flow is designed in such a way that the desired diagonalizations are precisely the equilibrium points in a given Cartan subalgebra. We characterize the set of all equilibria and establish a Morse-Bott type property ...

We introduce in this paper the concept of left WMC2 rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left HI rings can be extended to left WMC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with nonzero socle and extend some known results on ...

In this paper, we endow set S with the structure of an ordered semigroup and define “intuitionistic fuzzy” analogous for several notions that have been proved to be useful in the theory of ordered semigroups and give some equivalent conditions of these definitions. Then we characterize the completely regular and the strongly regular ordered semigroups by means of intuitionistic fuzzy bi-ideals.

As the main result of this paper it is proved that an interval matrix [Ac −∆, Ac +∆] is strongly regular if and only if the matrix inequality M(I − |I − RAc| − |R|∆) ≥ I has a solution, where M and R are real square matrices and M is nonnegative. Several consequences of this result are drawn.

In this paper, we construct a new infinite class of two-character sets in PG(5, q2) and determine their automorphism groups. From this construction arise new infinite classes of two-weight codes and strongly regular graphs, and a new distance-2 ovoid of the split Cayley hexagon of order 4.