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Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are ...
4.1 Graph theory. 4.2 Order theory. 5 Dynamical systems. ... Download as PDF; Printable version; ... (geometric group theory) Schreier's subgroup lemma;
The circle-based 1.1-skeleton (heavy dark edges) and 0.9-skeleton (light dashed blue edges) of a set of 100 random points in a square. In computational geometry and geometric graph theory, a β-skeleton or beta skeleton is an undirected graph defined from a set of points in the Euclidean plane.
It concerns straight-line embeddings of graphs in geometric spaces and graphs defined from configurations in a geometric space. See also Category:Topological graph theory for more general embeddings of graphs in surfaces, and Category:Graph drawing for the use of geometric representations in the visualization of graphs.
A drawing of the Petersen graph with slope number 3. In graph drawing and geometric graph theory, the slope number of a graph is the minimum possible number of distinct slopes of edges in a drawing of the graph in which vertices are represented as points in the Euclidean plane and edges are represented as line segments that do not pass through any non-incident vertex.
Graph duality is a topological generalization of the geometric concepts of dual polyhedra and dual tessellations, and is in turn generalized combinatorially by the concept of a dual matroid. Variations of planar graph duality include a version of duality for directed graphs, and duality for graphs embedded onto non-planar two-dimensional surfaces.
The polyhedral graph formed as the Schlegel diagram of a regular dodecahedron. In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron. Alternatively, in purely graph-theoretic terms, the polyhedral graphs are the 3-vertex-connected, planar graphs.
In set theory and graph theory, denotes the set of n-tuples of elements of , that is, ordered sequences of elements that are not necessarily distinct. In the edge ( x , y ) {\displaystyle (x,y)} directed from x {\displaystyle x} to y {\displaystyle y} , the vertices x {\displaystyle x} and y {\displaystyle y} are called the endpoints of the ...