Graphs

In analogy to the characterizations of the outerplanar and planar graphs as being the graphs with Colin de Verdière graph invariant at most two or three, the linklessly embeddable graphs are the graphs that have Colin de Verdière invariant at most four.

Noga Alon showed that certain graphs constructed from finite geometries are the sparsest examples of highly expanding graphs. citation Margulis-Gabber-Galil Algebraic constructions based on Cayley graphs are known for various variants of expander graphs.

Outerplanar graphs Outerplanar graphs are graphs with an embedding in the plane such that all vertices belong to the unbounded face of the embedding.

Complex graphs In the following graphs, the domain is the complex plane pictured, and the range values are indicated at each point by color.

Duals are useful because many properties of the dual graph are related in simple ways to properties of the original graph, enabling results to be proven about graphs by examining their dual graphs.

Graphs Graphs have path connected subsets, namely those subsets for which every pair of points has a path of edges joining them.

In contrast to polytopal graphs, graphs of arrangement polytopes are known to have small diameter, allowing the possibility of strongly polynomial-time criss-cross pivot algorithm without resolving questions about the diameter of general polytopes.

In these applications, graphs are ordered by specificity, meaning that more constrained graphs—which are more specific and thus contain a greater amount of information—are subsumed by those that are more general.

It is defined here for undirected graphs; for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge.

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.

So it suffices to prove the four color theorem for triangulated graphs to prove it for all planar graphs, and without loss of generality we assume the graph is triangulated.

Steinitz's theorem says that the polyhedral graphs formed from convex polyhedra are precisely the finite 3-connected simple planar graphs.

The mapping from strings to parse graphs is called parsing and the inverse mapping from parse graphs to strings is achieved by an operation that is called traversing the graph.

Topological spaces and graphs are special cases of connective spaces; indeed, the finite connective spaces are precisely the finite graphs.

Under the umbrella of social networks are many different types of graphs. citation Acquaintanceship and friendship graphs describe whether people know each other.

AMD's provided a couple of graphs to demonstrate what we're talking about here.

Experts do their best to predict it, brands make an effort to plan for it, people wearing suits in boardrooms point at line graphs, attempting with all their might to "forecast" it.

Harlee seems to come up with not only the headline and its link but two sets of graphs and the dead pool.

He advocated for detailing revenues and expenses on easy-to-understand graphs and charts, using percentages to convey the importance of each category.

Here are a few of the mortality-rate graphs as examples, with the blue color representing the “mortality deficit,” but anyone can go to the website and check any of the different countries and years.