In a visual cryptography scheme, a secret image is encoded inton shares, in the form of transparencies. The shares are then distributed to n participants. Qualified subsets of participants can recover the secret image by superimposing their transparencies, but non-qualified subsets of participants have no information about the secret image. Pixel expansion, which represents the number of subpixels in the encoding of the secret image, should be as small as possible. Optimal schemes are those that have the minimum pixel expansion. In this paper we study the pixel expansion of HYPERGRAPH access structures and introduce a number of upper bounds on the pixel expansion of special kinds of access structures. Also we demonstrate the minimum pixel expansion of induced matching HYPERGRAPH is sharp when every qualified subset is exactly one edge with odd size. Furthermore we explain that the minimum pixel expansion of every graph access structure Pn is exactly [n+1/2]. It indicates the lower bound mentioned in [4] is sharp.

A t-Cayley HYPERGRAPH X = t-Cay(G; S) is called normal for a finite group G, if the right regular representation R(G) of G is normal in the full automorphism group Aut(X) of X. In this paper, we investigate the normality of t-Cayley HYPERGRAPHs of abelian groups, where jSj  4.

We use the recursive method of construction large sets of t-designs given by Qiu-rong Wu (A note on extending t-designs, Australas. J. Combin., 4 (1991) 229 {235.), and present a similar method for constructingt -subset-regular self-complementary k -uniform HYPERGRAPHs of order v. As an application we show the existence of a new family of 2-subset-regular self-complementary 4-uniform HYPERGRAPHs with u=16 m+3.

In this paper, we call a HYPERGRAPH constructed by (non) binary linear\nonlinear codes a code-based HYPERGRAPH and study its properties. A transitive equivalence relation on any arbitrary code (as vertices) and its equivalence classes is defined as hyperedges of a HYPERGRAPH. This transitive relation, transfers the original information considered as a special code from the source in a form of subsets of special codes to hyper edges and therefore as a result, it puts each hyper edge in a one to one correspondence with a subset of special code. This research, shows that any transitive equivalence relation on codes provides a code-based HYPERGRAPH structure, and the significance of this topic is that the information in the form of linear\nonlinear codes can be transferred in different ways. Finally, this study relates code-based HYPERGRAPHs to code-based graphs via a binary relation, so that one could study and use its importance and application in different networks. In addition, one example of its application is introduced and described in wireless sensor networks.

In 1991, McKay and Radziszowski proved that, however each 3-subset of a 13-set is assigned one of two colours, there is some 4-subset whose four 3-subsets have the same colour. More than 25 years later, this remains the only non-trivial classical Ramsey number known for HYPERGRAPHs. In this article, we nd all the extremal colourings of the 3-subsets of a 12-set and list some of their properties. We also provide an answer to a question of Dudek, La Fleur, Mubayi and Rodl about the size-Ramsey numbers of HYPERGRAPHs.

In this paper we prove a generalized version of Hall's theorem in graphs, for HYPERGRAPHs. More precisely, let H be a k-uniform k-partite HYPERGRAPH with some ordering on parts as V1; V2; : : :; Vk such that the subHYPERGRAPH generated on ∪ k􀀀 1 i=1 Vi has a unique perfect matching. In this case, we give a necessary and sufficient condition for having a matching of size t = jV1j in H. Some relevant results and counterexamples are given as well.

In this paper, we de ne some new homomorphism-monotone parameters for hy-pergraphs. Using these parameters, we extend some graph homomorphism results to hyper-graph case. Also, we present some bounds for some well-known invariants of HYPERGRAPHs such as fractional chromatic number, independent numer and some other invariants of hyergraphs, in terms of these parameters.

In this note by considering a complete lattice L, we define the notion of an L-Fuzzy hyperrelation on a given non-empty set X. Then we define the concepts of (POM)_L-Fuzzy graph, HYPERGRAPH and subhypergroup and then obtain some related results. In particular we construct the categories of the above mentioned notions, and then give a (full and faithful) functor form the category of (POM)_L-Fuzzy subhypergroups ((POM)_L-Fuzzy graphs) into the category of (POM)_L-Fuzzy HYPERGRAPHs. Also we show that for each finite objects in the category of (POM)_L-Fuzzy graphs, the coproduct exists, and under a suitable condition the product exists too.

We consider a class of HYPERGRAPHs called hypercycles and we show that a hypercycle Cnd,a is shellable or sequentially the Cohen-Macaulay if and only if nÎ{3,5}. Also, we characterize Cohen-Macaulay hypercycles. These results are HYPERGRAPH versions of results proved for cycles in graphs.

Due to their structure and usage conditions, water meters face degradation, breaking, freezing, and leakage problems. There are various studies intended to determine the appropriate time to replace the degraded water meters. Earlier studies have used several features such as meteorological parameters, usage conditions, water network pressure, and structure of meters in order to detect the failed water meters. This article proposes a recommendation framework that uses the registered water consumption values as the input data and provides the meter replacement recommendations. This framework takes the time series of registered consumption values and pre-processes them in two rounds in order to extract the effective features. Then the multiple un-/semi-supervised outlier detection methods are applied to the processed data and assigns outlier/normal labels to them. At the final stage, a HYPERGRAPH-based ensemble method receives the labels and combines them to discover the suitable label. Due to the unavailability of the ground truth labeled data for meter replacement, we compare our method with respect to its FPR and two internal metrics: Dunn index and Davies-Bouldin index. The results of our comparative experiments show that the proposed framework detects more compact clusters with a smaller variance.