let  and  be banach algebras, ,  and . we define an -product on  which is a strongly splitting extension of  by . we show that these products form a large class of banach algebras which contains all module extensions and triangular banach algebras. then we consider spectrum, arens regularity, amenability and weak amenability of these products.

The automorphism group of the Zetterberg code Z length 17 (also a quadratic residue code) is rank three whose orbits on coordinate pairs determine two strongly regular graphs equivalent to Paley graph attached prime 17. As consequence, codewords given weight are characteristic vectors blocks PBIBD with associate classes cyclic type. More generally, this construction PBIBDs extended codes $$\equ...

We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanov’s conjecture by Ikuta and Munemasa [13].

A block negacyclic Bush-type Hadamard matrix of order 36 is used in a symmetric BGW(26, 25, 24) with zero diagonal over a cyclic group of order 12 to construct a twin strongly regular graph with parameters v=936, k=375, l=m=150 whose points can be partitioned in 26 cocliques of size 36. The same Hadamard matrix then is used in a symmetric BGW(50, 49, 48) with zero diagonal over a cyclic group o...

We construct two-intersection sets in PG(5, q), q odd, admitting PSL(2, q), whose associated strongly regular graphs have the same parameters as, but are not isomorphic to, Paley graphs.

E. R. van Dam gave an example of primitive non-amorphous association schemes in which every nontrivial relation is a strongly regular graph, as a fusion scheme of the cyclotomic scheme of class 45 on GF(212). The aim of this paper is to present a new example of primitive non-amorphous association schemes in which every nontrivial relation is a strongly regular graph, as a fusion scheme of the c...

Almost all finite graphs have the n-e.c. adjacency property, although until recently few explicit examples of such graphs were known. We survey some recently discovered families of explicit finite n-e.c. graphs, and present a new construction of strongly regular n-e.c. arising from affine planes.