# Graph

### graph theory (Teoría de grafos)

A simpler statement of the theorem uses graph theory.

It draws heavily on graph theory and mathematical logic.

Algebraic graph theory has close links with group theory.

### directed graph   (gráfico dirigido)

a directed graph where each edge has a weight of 1).

A current reality tree is a directed graph.

The terms rooted directed graph or rooted digraph also see variation in definitions.

### planar graph   (gráfico plano)

Conversely any planar graph can be formed from a map in this way.

The intuitive idea underlying discharging is to consider the planar graph as an electrical network.

The graph is the 1-skeleton of a cube, a cubical graph, a planar graph with eight vertices and twelve edges.

### undirected graph   (gráfico no dirigido)

If one views it as an undirected graph it is connected.

Thus, a "k"-coloring of an undirected graph "G" may be described by a homomorphism from "G" to the complete graph "K".

An Eulerian orientation of an undirected graph is an orientation in which each vertex has equal in-degree and out-degree.

### bipartite graph   (gráfica bipartita)

Every regular bipartite graph is also biregular.

Every complete bipartite graph formula_7 is formula_8-biregular.

A graphic matroid is bipartite if and only if it comes from a bipartite graph.

### complete graph

A tournament is an orientation of a complete graph.

It consists of a complete graph formula_1 minus one edge.

The complete graph has the best expansion property, but it has largest possible degree.

### given graph

The problem consists in deciding whether the given graph is connected or not.

Consider the computational problem of finding a coloring of a given graph "G".

A skew partition of a given graph, if it exists, may be found in polynomial time.