We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator represen...

We give two constructions of strongly regular Cayley graphs on finite fields Fq by using union of cyclotomic classes and index 2 Gauss sums. In particular, we obtain twelve infinite families of strongly regular graphs with new parameters.

Jacroux (1985) extended the definition of Regular graph designs of Mitchell and John (1976) to Semi-regular graph (SRG) designs, and studied the type 1 optimality of block designs. Here, the construction and optimality of some more SRG designs are discussed. Moreover, in this investigation, it is established that a class of two associate partially efficiency balanced design is, in fact SRG desi...

In [M. Klin, A. Munemusa, M. Muzychuk, P.-H. Zieschang Directed strongly regular graphs obtained from coherent algebras. Linear Algebra and its Applications 337, (2004) 83-109] the flag algebra of a given balanced incomplete block design with parameters (ν, b, r, k, λ) where λ = 1, has been constructed. In this paper, we consider the association scheme which is related to this flag algebra. By ...

We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.

If a symmetric association scheme of class two is realized as the symmetrization of a commutative association scheme, then it either admits a unique symmetrizable fission scheme of class three or four, or admits three fission schemes, two of which are class three and one is of class four. We investigate the classification problem for symmetrizable (commutative) association schemes of two-class ...

Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence matrix of a symmetric design and the all-ones matrix. Amorphous pseudocyclic association schemes are examples of such association schemes whose associated sym...

Let Γ be a distance-regular graph with diameterd ≥ 3 and heighth = 2, whereh = max{i : pd,i 6= 0}. Suppose that for every α in Γ and every β in Γd(α), the induced subgraph on Γd(α)∩ Γ2(β) is isomorphic to a complete multipartite graph Kt×2 with t ≥ 2. Then d = 4 and Γ is isomorphic to the Johnson graph J(10, 4).

The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is introduced which is very simple and easy to implement, but very efficient in discriminating non-isomorphic graphs, in practice. This method does not need any ...