Figure concepts and types
Concept map
FIG is a collection of interconnected nodes
As shown, a map may be this:
FIG There node (node) and the edge (Edge). Between nodes connected by edges to each other.
Defined tuple
G is an ordered tuple (V, E), where V is called a top collector (Vertices Set), E is called the set of edges (Edges set), E and V do not intersect. They may also be written as V (G) and E (G).
The type of graph
Directed graph and undirected graph
If each edge to FIG no predetermined direction, resulting undirected graph referred to in FIG.
In the figure, indicated by arrows when the edge is directional, from start to finish, so called a directed graph in FIG.
In above figure, G1 undirected graph, G2 is a directed graph.
Figure G1:
Figure G2:
DAY
Refers to a loop after the other from a starting point has returned to the origin point, such as the following from the point A to FIG. B through C may be returned to A, a loop is formed:
Directed acyclic graph (Directed Acyclic Graph) refers to a loop-free directed graph. :
AOV
Vertex activities Net (Activity On Vertex Network) refers to the project have a representation with vertices represent activities to the figure, the priority between activities with the arc. Such a directed graph vertices represent the activities of the network.
Complete Graph
n vertices, n (n-1) / 2 and is not repeated in FIG sides and edges of the ring, referred to as completely to FIG.
Having n vertices, n (n-1) have edges directed graph, known as fully to FIG.
Completely and entirely undirected graph directed graph is called a complete graph.
Euler
Euler (Euler Graph) refers to the communication through FIG G = <V, E> and only once on each side by a passage (undirected or directed graph) of all the edges, called Euler corresponding circuit.
FIG called Euler, without having Euler path having Euler having Euler called half Euler FIG.
- An undirected graph G is Euler if and only if G is connected, and the degree of non-singular vertex.
- A digraph D is Euler if and only if D is connected, and all the vertices of an equal degree.
Hamiltonian
FIG Hamilton (Hamilton Graph) by G = <V, E>, G is elapsed for each vertex once and only once referred to as passage Hamilton path through each vertex once and only once called Hamilton loop circuit.
FIG Hamilton circuit having referred to FIG Hamilton, without having a passage having a Hamilton Hamilton circuit called a half-Hamilton FIG.
No simple Hamilton graphs necessary and sufficient conditions, necessary and sufficient conditions are a problem in graph theory.
On FIG U.S. mathematician 1960. Ole given in a graph of FIG Hamilton sufficient condition: the number of vertices is larger than for FIG. 2, if any two of the figures and equal to or greater than the total number of vertices, then this must FIG. It is Hamiltonian.
FIG communication
FIG communication (Connected Graph) refers to any of the figures are two communication nodes. FIG communication refers to the G = <V, E>, if from vertex i to vertex j is connected with a path, called i and j are connected.
Strong graph
Strong graph (Strongly Connected Graph) refers to the FIG. G = <V, E> is a connected graph, and this graph is a directed graph.
