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An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...
Knowledge graph completion (KGC) is a collection of techniques to infer knowledge from an embedded knowledge graph representation. [11] In particular, this technique completes a triple inferring the missing entity or relation. [11]
A toroidal graph is a graph that can be embedded without crossings on the torus. More generally, the genus of a graph is the minimum genus of a two-dimensional surface into which the graph may be embedded; planar graphs have genus zero and nonplanar toroidal graphs have genus one. Every graph can be embedded without crossings into some ...
These graphs include the complete graph K 6, the Petersen graph, the graph formed by removing an edge from the complete bipartite graph K 4,4, and the complete tripartite graph K 3,3,1. Every planar graph has a flat and linkless embedding: simply embed the graph into a plane and embed the plane into space. If a graph is planar, this is the only ...
In mathematics, topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. [1] It also studies immersions of graphs. Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for example, without two edges ...
A cubic graph with 14 vertices embedded on a torus The Heawood graph and associated map embedded in the torus. In the mathematical field of graph theory, a toroidal graph is a graph that can be embedded on a torus. In other words, the graph's vertices and edges can be placed on a torus such that no edges intersect except at a vertex that ...
Puppet can produce DOT resource graphs that can be viewed with Graphviz. Scribus is an open-source DTP program that can use Graphviz to render graphs by using its internal editor in a special frame type called render frame. [11] Sphinx is a documentation generator that can use Graphviz to embed graphs in documents.
The surface onto which the graph is embedded may be determined by whether it is orientable (true if any cycle in the graph has an even number of twists) and by its Euler characteristic. The embeddings that can be represented by ribbon graphs are the ones in which a graph is embedded onto a 2- manifold (without boundary) and in which each face ...