Aspect-orientation is a relatively new paradigm that introduces abstractions to modularize the implementation of system-wide policies. It is based on a composition operation, called aspect weaving, that implicitly modifies a base system by performing related changes within the system modules. Aspect-oriented graph grammars (AOGG) extend the classic graph grammar formalism by defining aspects as...

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...

In this paper we study the problem of recognizing and representing dynamically changing proper interval graphs. The input to the problem consists of a series of modifications to be performed on a graph, where a modification can be a deletion or an addition of a vertex or an edge. The objective is to maintain a representation of the graph as long as it remains a proper interval graph, and to det...

In this work, we extend the formulation of spatial-based graph convolutional networks with a new architecture, called graph-informed neural network (GINN). This architecture is specifically designed for regression tasks on graph-structured data that are not suitable well-known networks, such as functions domain and codomain defined two sets values vertices graph. particular, formulate (GI) laye...

Consider the maximum length [(k) of a flexicographieally) increasing sequence of vectors in GF(2) k with the property that the sum of the vectors in any consecutive subsequence is nonzero modulo 2. We prove that ~ . 2 k ~<f(k)~<(~+o(1))2 k. A related problem is the following. Suppose the edges of the complete graph K , are labelled by the numbers 1,2 . . . . . (~.). What is the minimum a(n), ov...

With every σ-ideal I on a Polish space we associate the σ-ideal generated by closed sets in I. We study the forcing notions of Borel sets modulo the respective σ-ideals and find connections between their forcing properties. To this end, we associate to a σ-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the...

In 1969, White conjectured that the orientable genus of the complete tripartite graph Kl,m,n, with l ≥ m ≥ n, is ⌈ (l−2)(m+n−2) 4 ⌉ . In this talk we describe progress on this conjecture. We can show that White’s conjecture is true in the cases where (m, n), reduced modulo 4, is (0, 0), (0, 2), (1, 1), (2, 0), (2, 1), (2, 2), (2, 3) or (3, 3). We discuss similarities and differences between our...

For any natural number k, a graph G is said to be pancyclic mod k if it contains a cycle of every length modulo k. In this paper, we show that every K1,4-free graph G with minimum degree δ(G) ≥ k+ 3 is pancyclic mod k and every claw-free graph G with δ(G) ≥ k+ 1 is pancyclic mod k, which confirms Thomassen’s conjecture [8] for claw-free graphs.

Let m 6= n. An m × n × p proper array is a three-dimensional array composed of directed cubes that obeys certain constraints. Because of these constraints, the m × n × p proper arrays may be classified via a schema in which each m × n × p proper array is associated with a particular m × n planar face. By representing each connencted component present in the m × n planar face with a distinct let...