This article is about the study of graph embeddings. For graphs in the plane with crossings, see topological graph.
Animation detailing the embedding of the Pappus graph and associated map in the torus
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 intersecting. A basic embedding problem often presented as a mathematical puzzle is the three utilities problem. Other applications can be found in printing electronic circuits where the aim is to print (embed) a circuit (the graph) on a circuit board (the surface) without two connections crossing each other and resulting in a short circuit.
mathematics, topologicalgraphtheory is a branch of graphtheory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological...
crossing). A topologicalgraph is also called a drawing of a graph. An important special class of topologicalgraphs is the class of geometric graphs, where...
In mathematics, particularly graphtheory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it...
In topologicalgraphtheory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation...
topologicalgraphs, where the edges are allowed to be arbitrary continuous curves connecting the vertices; thus, it can be described as "the theory of...
mathematical discipline of graphtheory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...
In graphtheory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges, vertices and by contracting edges...
the mathematical field of graphtheory, a toroidal graph is a graph that can be embedded on a torus. In other words, the graph's vertices and edges can be...
correlation functions do not change. Consequently, they are topological invariants. Topological field theories are not very interesting on flat Minkowski spacetime...
Appendix:Glossary of graphtheory in Wiktionary, the free dictionary. This is a glossary of graphtheory. Graphtheory is the study of graphs, systems of nodes...
In topologicalgraphtheory, a ribbon graph is a way to represent graph embeddings, equivalent in power to signed rotation systems or graph-encoded maps...
In topologicalgraphtheory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional...
number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the...
In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles. They were discovered...
In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies...
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