It is known that a strongly regular semi-Cayley graph (with respect to a group G) corresponds to a triple of subsets (C, D, D') of G. Such a triple (C, D, D') is called a partial difference triple. First, we study the case when D U D' is contained in a proper normal subgroup of G. We basically determine all possible partial difference triples in this case. In fact, when \G\ f 8 nor 25, all part...

Intriguing sets of vertices have been studied for several classes of strongly regular graphs. In the present paper, we study intriguing sets for the graphs Γn, n ≥ 2, which are defined as follows. Suppose Q(2n, 2), n ≥ 2, is a nonsingular parabolic quadric of PG(2n, 2) and Q+(2n − 1, 2) is a nonsingular hyperbolic quadric obtained by intersecting Q(2n, 2) with a suitable nontangent hyperplane. ...

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.

Let Γ be a distance-regular graph with diameter d and Kneser graph K = Γd, the distance-d graph of Γ. We say that Γ is partially antipodal when K has fewer distinct eigenvalues than Γ. In particular, this is the case of antipodal distance-regular graphs (K with only two distinct eigenvalues), and the so-called half-antipodal distance-regular graphs (K with only one negative eigenvalue). We prov...

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...

A graph G has constant μ = μ(G) if any two vertices that are not adjacent have μ common neighbours. G has constant μ and μ if G has constant μ = μ(G), and its complement G has constant μ = μ(G). If such a graph is regular, then it is strongly regular, otherwise precisely two vertex degrees occur. We shall prove that a graph has constant μ and μ if and only if it has two distinct restricted Lapl...

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 ...