Diagrams that serve as a visual input facility for programming environments have to be translated into some kind of semantic description. This paper describes such a method which is based on a specification of the translation process. The translation process starts with a diagram, which is simply represented as a collection of atomic diagram components, and it ends up with some data structure a...

For a positive integer q, a k-uniform hypergraph X = (V,E) is q-complementary if there exists a permutation θ on V such that the sets E,E, E 2 , . . . , E q−1 partition the set of k-subsets of V . The permutation θ is called a q-antimorphism of X. The well studied self-complementary uniform hypergraphs are 2-complementary. For an integer n and a prime p, let n(p) = max{i : p i divides n}. In th...

When working with diagrams in visual environments like graphical diagram editors, diagrams have to be represented by an internal model. Graphs and hypergraphs are well-known concepts for such internal models. This paper shows how hypergraphs can be uniformly used for a wide range of different diagram types where hyperedges are used to represent diagram components as well as spatial relationship...

Sketching, i.e., drawing diagrams by hand and directly on the screen, is gaining popularity, as it is a comfortable and natural way to create and edit diagrams. Hand drawing is inherently imprecise, and often sloppy. As a consequence, when processing hand drawn diagrams with a computer, ambiguities arise: it is not always clear what part of the drawing is meant to represent what component. Reso...

DiaGen is a specification method, which is primarily based on a hypergraph grammar, and a tool that allows to automatically generate diagram editors from such a specification. Generated editors are free-hand editors, but with an automatic, constraint-based layout for correct diagrams. A hypergraph parser checks diagram correctness and makes it possible to translate diagrams into some user-defin...

Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms assumed pairwise relationships objects interest. However, many real applications, the between are higher-order, beyond a formulation. To efficiently learn deep embeddings on high-order graph-structured data, we introduce two end-to-end trainable ...

for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.

In this paper we examine the orders of vertex-transitive self-complementary uniform hypergraphs. In particular, we prove that if there exists a vertex-transitive selfcomplementary k-uniform hypergraph of order n, where k = 2 or k = 2 + 1 and n ≡ 1 (mod 2), then the highest power of any prime dividing n must be congruent to 1 modulo 2. We show that this necessary condition is also sufficient in ...

In this paper, we introduce certain concepts, including neutrosophic hypergraph, line graph of neutrosophic hypergraph, dual neutrosophic hypergraph, tempered neutrosophic hypergraph and transversal neutrosophic hypergraph. We illustrate these concepts by several examples and investigate some of interesting properties. Key-words: Neutrosophic hypergraph, Line graph of neutrosophic hypergraph, D...

Given an undirected hypergraph and a subset of vertices S ⊆ V with a specified root vertex r ∈ S, the Steiner Rooted-Orientation problem is to find an orientation of all the hyperedges so that in the resulting directed hypergraph the “connectivity” from the root r to the vertices in S is maximized. This is motivated by a multicasting problem in undirected networks as well as a generalization of...