a graph has two sets:
♦ The set V (Vertex) that its elements are called vertices (or
points or nodes or points)
♦ The set E (Edge), which is not sequential pairs of
node, its members called segments (ribs or sides)
Notation: G (V, E)
Vertices u and v are called adjacent if there is a segment (u, v). Graphs can also be
presented geometrically, the node is presented as a point, while the segment is presented
as a line connecting two vertices.
Example 1:
Graph G (V, E) with:
1. V consists of four nodes, namely node A, B, C and D
2. E consists of five segments, namely e1 = (A, B) e2 = (B, C) e3 = (A, D)
e4 = (C, D) e5 = (B, D)
Many knot called ORDER, many segments of the graph is called SIZE.
GRAPHBERLABEL
Labeled graph G is called a graph or if the segment and the noose was associated with a
certain magnitude. If each segment e of G is associated with a non-negative number d (e),
then d (e) is called the weight
or the length of the segment e.
DEGREES Graf
The degree of vertex V, written d (v) is the number of the contact segment v. Since each
segment counted twice when determining the degree of a graph, then:
The number of degrees of all vertices of a graph (degrees) = two times
large segment of the graph (graph size).
A knot is called the even / odd depending on whether the degree of a node is an even /
odd. If there is a self-loop, then the self-loop is calculated two times the degrees of
vertices.
Example:
Here the number segment = 7, whereas the degree of each
node is:
d (A) = 2 d (D) = 3 degrees of a graph G = 14
d (B) = 5 d (E) = 1 (2 * 7)
d (C) = 3 d (F) = 0
Note: E is called a node depends / end, the node
degree one. While F is called a remote node, ie
vertices of degree zero.
Connectedness
Walk or travel in a graph G is the line of nodes and
alternating segments: v1, e1, v2, e2, ..., en-1, v
Here e1 segment connecting vertices vi and vi +1
The number of segments is called the long walk.
Walk can be written more briefly by simply writing a row
segments: e1, e2, ..., en-1
or a row of vertices: v1, v2, ..., vn-1, v
v1 is called the initial node, v is called the final node
Walk is called closed if v1 = vn, on the other so-called walk
open, connecting v1 and vn
Trail is a walk with all the segments in different rows.
Path or a path is a walk with all vertices in a row
is different. So surely dirt path, while the trail is not necessarily the path.
In other words: A path is a trail open to
degrees per knot = 2, except the initial node v1 and node v
final degree = 1.
Cycle or circuit is a closed trail with the degree of each
node = 2