We derive strong structural constraints on the automorphism groups of strongly regular (s. r.) graphs, giving a surprisingly strong answer to a decades-old problem, with tantalizing implications to testing isomorphism of s. r. graphs, and raising new combinatorial challenges. S. r. graphs, while not believed to be Graph Isomorphism (GI) complete, have long been recognized as hard cases for GI, ...

The fundamental properties of the class QUASI of quasi-relabeling relations are investigated. A quasi-relabeling relation is a tree relation that is de ned by a tree bimorphism (φ,L, ψ), where φ and ψ are quasi-relabeling tree homomorphisms and L is a regular tree language. Such relations admit a canonical representation, which immediately also yields that QUASI is closed under nite union. Howe...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

in this paper, a commutative semigroup will be written as a disjoint :union: of its cancellative subsemigroups. based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.

This paper deals with a class of 2-step solvable simply connected Lie groups G in which we construct certain lattices Γ . It turns out that these are all the lattices in such groups. We then apply our results to study the decomposition of the quasi-regular representation of G on G/Γ .

We prove the weak-∗ convergence of a certain sequence of averages of unitary operators associated to the action of the free group on its Gromov boundary. This result, which can be thought as an ergodic theorem à la von Neumann with coefficients, provides a new proof of the irreducibility of the quasi-regular representation of the free group.