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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 ...
The theory of topological graphs is an area of graph theory, mainly concerned with combinatorial properties of topological graphs, in particular, with the crossing patterns of their edges. It is closely related to graph drawing , a field which is more application oriented, and topological graph theory , which focuses on embeddings of graphs in ...
Topological graph theory is a branch of graph theory. Its main topic is the study of embeddings of graphs in surfaces. Its main topic is the study of embeddings of graphs in surfaces. See also Category:Geometric graph theory and Category:Graph drawing
The associated topological space of a graph is connected (with respect to the graph topology) if and only if the original graph is connected.; Every connected graph contains at least one maximal tree , that is, a tree that is maximal with respect to the order induced by set inclusion on the subgraphs of which are trees.
2. Topological graph theory is the study of graph embeddings. 3. Topological sorting is the algorithmic problem of arranging a directed acyclic graph into a topological order, a vertex sequence such that each edge goes from an earlier vertex to a later vertex in the sequence. totally disconnected Synonym for edgeless. tour
This is in analogy to the Petersen family, which too is named after its member the Petersen graph. The Heawood families are significant in topological graph theory. They contain the smallest known examples of intrinsically knotted graphs, [1] of graphs that are not 4-flat, and of graphs with Colin de Verdière graph invariant =.
A graph H is called a topological minor of a graph G if a subdivision of H is isomorphic to a subgraph of G. [21] Every topological minor is also a minor. The converse however is not true in general (for instance the complete graph K 5 in the Petersen graph is a minor but not a topological one), but holds for graph with maximum degree not ...
The Heawood graph and associated map embedded in the torus.. In topological graph theory, an embedding (also spelled imbedding) of a graph on a surface is a representation of on in which points of are associated with vertices and simple arcs (homeomorphic images of [,]) are associated with edges in such a way that: