Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for these three graphs the bound k ≤ (n − 1)/2 holds. This result implies that only one of a complem...

The exponent puzzle of the Anderson-Mott transition is discussed on the basis of a duality model for strongly correlated electrons.

Our general investigation of universal algebras obtained from multialgebras via strongly regular equivalence relations provides useful general results concerning fuzzy set topics related to multialgebra theory. We also give many hints on how to connect our approach with the results from the literature. Acknowledgement. The first author was supported by the CNCS-UEFISCDI grant PNII-RU-TE-2011-3-...

We present new abelian partial difference sets and amorphic group schemes of both Latin square type and negative Latin square type in certain abelian p-groups. Our method is to construct what we call pseudo-quadratic bent functions and use them in place of quadratic forms. We also discuss a connection between strongly regular bent functions and amorphic group schemes.

In this note we prove that bent functions can be precisely characterized in terms of a special class of strongly regular graphs, thus providing a positive answer to a question raised in the paper Spectral Analysis of Boolean Functions as a Graph Eigenvalue Problem. (After publication of the above paper by the rst two authors, the third sent them a remark showing that bent functions are exactly ...

In this paper, we completely determine the connectivity of every infinite circulant digraphs and prove that almost all infinite circulant digraphs are infinitely strongly connected and therefore have both oneand two-way infinite Hamiltonian paths.

A convex polygon in R 2 , or a convex polyhedron in R 3 , will be called a tile. A connected set P of tiles is called a partial tiling if the intersection of any two of the tiles is either empty, or is a vertex or edge (in R 3 : or face) of both. P is called strongly normal (SN) if, for any partial tiling P 0 P and any tile P 2 P 0 , the neighborhood N(P; P) of P (the union of the tiles of P 0 ...

Abnormal isoforms of the prion protein (PrP(Sc)) that cause prion diseases are propagated and spread within the body by "carrier" cell(s). Cells of the immune system have been strongly implicated in this process. In particular, PrP(Sc) is known to accumulate on follicular dendritic cells (FDCs) in individuals affected by variant Creutzfeld-Jakob disease. However, FDCs do not migrate widely and ...