Related papers: Index notation of grid graphs
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
Trace diagrams are structured graphs with edges labeled by matrices. Each diagram has an interpretation as a particular multilinear function. We provide a rigorous combinatorial definition of these diagrams using a notion of signed graph…
Crossword puzzles lend themselves to mathematical inquiry. Several authors have already described the arrangement of crossword grids and associated combinatorics of answer numbers. In this paper, we present a new graph-theoretic…
We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…
We use grid diagrams to present a unified picture of braids, Legendrian knots, and transverse knots.
This article provides structural characterization of simple graphs whose edge-set can be partitioned into maximum matchings. We use Vizing's classification of simple graphs based on edge chromatic index.
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs
Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation,…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…
In this paper we present a characterisation, by an infinite family of minimal forbidden induced subgraphs, of proper circular arc graphs which are intersection graphs of paths on a grid, where each path has at most one bend (turn).
A grid drawing of a graph maps vertices to grid points and edges to line segments that avoid grid points representing other vertices. We show that there is a number of grid points that some line segment of an arbitrary grid drawing must…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
The concept of n-categories and related subject is considered. An n-category is described as an n-graph with a composition. A new definition of operad is presented. Some illustrative examples are given.
Let G be an arbitrary simple graph. The main results are explicit representations of the edge cone of G as a finite intersection of closed halfspaces. If G is bipartite and connected we determine the facets of the edge cone and present a…
Let G be a simple finite graph such that each vertex has an integer value and different vertices have different values. Let S be a finite non-empty set of primes. We call G an S-graph if any two vertices are connected by an edge if and only…