First, Fig.
1, the basic concept of FIG.
Handshake theorem: undirected graph, the number of all edge nodes to twice the sum of the degree
A directed graph, and all nodes equal to the sum of the number of sides equal to the sum of
Corollary: Any map has an even number of odd nodes
FIG various (V, E) = (n, m)
| Zero Figure |
Only isolated FIG nodes |
| Trivial graph |
Zero-order diagram |
| Regular Graphs k |
All nodes of degree k are undirected graph |
| Completely undirected graph |
k = n - Regular Figure 1; number of edges = C (n, 2) |
| Complete directed graph |
All of the nodes of an == == n - 1, the number of edges = A (n, 2) |
Path: start and end points are not the same
Loop: start and end the same
Base path - path length is not substantially duplicate FIG point --n Order <= n - 1
Simple path - no duplicate edge
2, FIG matrix representation of the information carried in the matrix &&
eg adjacency matrixのFIG characteristics
Communication / strong graph - reachability matrix (matrix may transitive closure) a whole
3, the connectivity of FIG.
Undirected graph - do not communicate communication /
Digraph - / unidirectional communication communicating strong / weak communication
4, the application-related map of FIG. & Special
1) Hamilton FIG.
Sufficient Conditions: any u, v belongs to V, d (u) + d (v)> = n, n is the number of vertices and n> = 3
Requirements: ...
application:
Determining the presence of a Hamiltonian graph
2 obtained Hamill path / circuit
eg1 Given a cube map, find Hamilton loop
eg2 arrangements examination schedule
Six days to arrange 6 courses, ABCDEF, test, test day one, assuming elective cases are:
How DCA BCF EB AB to schedule such that no two people are the same day exam?
2) two in FIG.
And sufficient conditions:
- The collection is divided into two parts, there is no direct connection between the points of each part, and only part of the cross-connection
Requirement
- All loops are even-length
nature:
FIG complete two sides number e = | V1 | * | V2 |
3) FIG Euler
Containing Euler circuit with or without directed graph called a directed graph Euler
n is odd, undirected graph nontrivial completely Euler FIG.
Second, the tree
の binary tree defined: a rooted tree, the node 2 is not zero degree
Prefix: each symbol string and do not prefixed
Undirected tree: No loop-free communication to FIG.