We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that the category formed by these decompositions with certain morphisms is equivalent to the category of strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence, each ideal regular language is the set ...

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.

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

A graph is 3-e.c. if for every 3-element subset S of the vertices, and for every subset T of S, there is a vertex not in S which is joined to every vertex in T and to no vertex in S \ T. Although almost all graphs are 3-e.c., the only known examples of strongly regular 3-e.c. graphs are Paley graphs with at least 29 vertices. We construct a new infinite family of 3-e.c. graphs, based on certain...

In this note we introduce a new equivalence relation θ∗ on a (semi)hyperring R and we show that it is strongly regular. Also we prove that, R/θ∗, the equivalence class of this equivalence relation under usual operations consists a commutative (semi-)ring. Finally we introduce the notion of θ-parts of hyperrings and investigate the important properties of them. Mathematics Subject Classification...

We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some ...

Definition of the strongly regular graphs on 77 and 100 vertices belonging to the simple groups M22 and HiS.

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.

We consider directed strongly regular graphs de2ned in 1988 by Duval. All such graphs with n vertices, n6 20, having a vertex-transitive automorphism group, are determined with the aid of a computer. As a consequence, we prove the existence of directed strongly regular graphs for three feasible parameter sets listed by Duval. For one parameter set a computer-free proof of the nonexistence is pr...