Notions of strongly regular, regular and left(right) regular $Gamma$−semigroupsare introduced. Equivalent conditions are obtained through fuzzy notion for a$Gamma$−semigroup to be either strongly regular or regular or left regular.

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...

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 ...

We introduce canonical principal parameters on any strongly regular minimal surface in the three dimensional sphere and prove that any such a surface is determined up to a motion by its normal curvature function satisfying the Sinh-Poisson equation. We obtain a classification theorem for bi-umbilical hypersurfaces of type number two. We prove that any minimal hypersurface of type number two wit...

We prove cocompleteness of the category of CASL signatures , of monotone signatures, of strongly regular signatures and of strongly locally ltered signatures. This shows that using these signature categories is compatible with a pushout or colimit based module system.

The existence of a partial quadrangle PQ(s, t, μ) is equivalent to the existence of a diamond-free strongly regular graph SRG(1+s(t+1)+s2t(t+1)/μ, s(t+1), s−1, μ). Let S be a PQ(3, (n + 3)(n2 − 1)/3, n2 + n) such that for every two non-collinear points p1 and p2, there is a point q non-collinear with p1, p2, and all points collinear with both p1 and p2. In this article, we establish that S exis...

In this paper, we begin the determination of all primitive strongly regular graphs with chromatic number equal to 5. Using eigenvalue techniques, we show that there are at most 43 possible parameter sets for such a graph. For each parameter set, we must decide which strongly regular graphs, if any, possessing the set are 5-chromatic. In this way, we deal completely with 34 of these parameter se...

We present 15 new partial difference sets over 4 non-abelian groups of order 100 and 2 new strongly regular graphs with intransitive automorphism groups. The strongly regular graphs and corresponding partial difference sets have the following parameters: (100,22,0,6), (100,36,14,12), (100,45,20,20), (100,44,18,20). The existence of strongly regular graphs with the latter set of parameters was a...